The scale factor is 1/3.
What is the scale factor?
The difference in scale between an original object's scale and a new object that is its representation but is larger or smaller is known as a scale factor. For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2.
Here, we have
Given: Triangle D has been dilated to create triangle D′.
To find the scalar value, simply choose one side of D and one did of D’ and divide them to find the scalar. We can verify that we have the correct scalar by performing this division on each related edge. Below I will do D to D’ represented like D/D’:
4.8 / 1.6 = 3
4.2 / 1.4 = 3
2.7 / x = 3
Knowing that the scaling for each edge is 3, we can solve for x.
2.7 / 3 = x
0.9 = x
The edges for D are 4.8, 4.2, and 2.7 respectively to D’ scaled by 1/3. So we can determine that the edges for D’ are 1.6, 1.4, and 0.9 respectively to D scaled by 3.
So if we go D’ to D, we scale by 3. If we go D to D’, we scale by 1/3.
Hence, the scale factor is 1/3.
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50 Points! Write the expression x^4+5x^2-8 in quadratic form, if possible. Photo attached. Thank you!
The expression x^4 + 5x^2 - 8 in quadratic form is: (x^2 + 8)(x^2 - 1)
How to solve the expressionIt should be noted that to express the given expression x^4+5x^2 - 8 in quadratic form, we need to identify a suitable substitution that will allow us to rewrite the expression as a quadratic in a new variable.
One possible substitution is to let u = x^2, so that we can write:
x^4 + 5x^2 - 8 = u^2 + 5u - 8
We can then factor this quadratic expression as:
u^2 + 5u - 8 = (u + 8)(u - 1)
Substituting back u = x^2, we get:
x^4 + 5x^2 - 8 = (x^2 + 8)(x^2 - 1)
Therefore, the expression x^4 + 5x^2 - 8 in quadratic form is:
(x^2 + 8)(x^2 - 1)
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Ejercicio 2.- La temperatura ambiente a las 8 am era de 61 grados Farenheit. Fue aumentando de forma lineal hasta la 1 pm en que el termómetro marcó 81 grados. a) Escriba una ecuación lineal que muestre la temperatura en función de la hora en ese intervalo. b) Calcule con esa ecuación la temperatura a las 11:15 am. Aproxime a la décima de grado Farenheit si fuera necesario. oprondamos a hacer ecuaciones y resolver
a)Por lo tanto, la ecuación lineal que representa la temperatura en función de la hora es T(h) = 4h + 29
b) Por lo tanto, la temperatura a las 11:15 am aproximadamente es de 75.3 grados Farenheit.
what is aproximadamente ?
"Aproximadamente" is a Spanish word that means "approximately" or "roughly" in English. It is often used to indicate that a value or measurement is not exact, but rather an estimation or approximation.
In the given question,
a) La ecuación lineal que relaciona la temperatura con la hora en ese intervalo es:
T(h) = m*h + b
donde T es la temperatura en grados Farenheit, h es la hora en formato de 24 horas, m es la pendiente de la recta y b es el término independiente.
Primero encontramos la pendiente m:
m = (81 - 61) / (13 - 8) = 4
Luego, encontramos el término independiente b utilizando uno de los puntos:
61 = 4*8 + b
b = 29
Por lo tanto, la ecuación lineal que representa la temperatura en función de la hora es:
T(h) = 4h + 29
b) Para encontrar la temperatura a las 11:15 am, primero convertimos el tiempo a horas decimales:
11:15 am = 11 + 15/60 = 11.25 horas
Luego, sustituimos este valor en la ecuación lineal:
T(11.25) = 4(11.25) + 29 = 75.25
Por lo tanto, la temperatura a las 11:15 am aproximadamente es de 75.3 grados Farenheit.
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Choose the expression that correctly compares the numbers 117 and 171.
171 < 117
171 = 117
171 > 117
117 > 171
Answer:
171 > 117
Step-by-step explanation:
171 is greater than 117 meaning the alligator is eating the bigger number, 171.
Trangle ABC has an area 25 square feet and perimeter of 65.5 feet of triangle ABC is dilated by a factor of 5/2 to create now calculate the area of trangle DEF using the scale factor
So, the area of triangle DEF is 312.5 square feet, using the scale factor of 5/2.
What is dilation?the context of mathematics and geometry, dilation is a transformation that changes the size of an object. It is a type of transformation that scales an object by a certain factor, without changing its shape or orientation.
In other words, dilation involves multiplying the coordinates of a geometric figure by a fixed constant, which results in an enlarged or reduced version of the original figure. The constant is known as the dilation factor or the scale factor, and it can be any real number greater than zero.
For example, if we dilate a circle by a scale factor of 2, every point on the circle will be moved twice as far away from the center, resulting in a new circle with a diameter twice as large as the original.
Let's start by using the formula for the perimeter of a triangle:
[tex]Perimeter of triangle ABC = AB + BC + AC = 65.5 feet[/tex]
We can also use Heron's formula to find the area of triangle ABC:
[tex]Area of triangle ABC = \sqrt(s(s-AB)(s-BC)(s-AC))[/tex]
where s is the semi perimeter of the triangle:
[tex]s = (AB + BC + AC) / 2[/tex]
We can use these equations to solve for the side lengths of triangle ABC:
[tex]AB + BC + AC = 65.5[/tex]
[tex]s = (AB + BC + AC) / 2[/tex]
[tex]25 = \sqrt(s(s-AB)(s-BC)(s-AC))[/tex]
Solving for AB, BC, and AC gives us:
AB = 15
BC = 20
AC = 30.5
Now, let's dilate triangle ABC by a factor of 5/2 to create triangle DEF. This means that each side of triangle ABC will be multiplied by 5/2 to get the corresponding side length of triangle DEF.
DE = AB * (5/2) = 37.5
EF = BC * (5/2) = 50
DF = AC * (5/2) = 76.25
Now we can use Heron's formula again to find the area of triangle DEF:
s = (DE + EF + DF) / 2 = 81.875
Area of triangle DEF = sqrt(s(s-DE) (s-EF) (s-DF)) = 312.5 square feet
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Ashley is reading a book for her English class. The graph shows the number of pages she needs to read in 30 hours in order to finish reading the book. How many pages does Ashley need to read every 10 hours
With the help of slope we conclude that Ashley needs to read 100 pages every 10 hours to finish the book in 30 hours.
What is slope?Slope is a measure of the steepness of a line, and is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.
According to given information:To find out how many pages Ashley needs to read every 10 hours, we need to look at the slope of the line on the graph. The slope tells us the rate of change of the number of pages read per hour.
We can use the formula for slope, which is:
slope = (change in y) / (change in x)
In this case, the "change in y" is the number of pages Ashley needs to read in 30 hours minus the number of pages she needs to read in 0 hours (which is the starting point of the graph). The "change in x" is 30 hours minus 0 hours. So we have:
slope = (number of pages in 30 hours - number of pages in 0 hours) / (30 hours - 0 hours)
Using the graph, we can see that the number of pages Ashley needs to read in 30 hours is 300. The number of pages she needs to read in 0 hours (or the starting point of the graph) is 0. So we have:
slope = (300 - 0) / (30 - 0) = 10
This means that Ashley needs to read 10 pages per hour to finish the book in 30 hours. To find out how many pages she needs to read every 10 hours, we can multiply the hourly rate by 10:
10 pages per hour * 10 hours = 100 pages
Therefore, Ashley needs to read 100 pages every 10 hours to finish the book in 30 hours.
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Cual es el valor de p(B/A)?
The value of p(B/A) represents the probability that event B will occur given that event A has occurred.
What is the probability?It is a measure of conditional probability, which is calculated using the formula:
p(B/A) = p(A ∩ B) / p(A)
Where:
p(A ∩ B) is the probability that both events A and B occur together, that is, the intersection of A and B.p(A) is the probability that event A will occur.Therefore, To calculate the value of p(B/A), you need to know the probabilities of A and B, as well as the probability that both occur together.
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If a population of yeast cells grows from 5 to 160 in a period of five hours, what is the rate of growth
Answer:
The population of yeast cells is growing at a rate of approximately 46.41% per hour.
Step-by-step explanation:
To find the rate of growth of the yeast population, we can use the exponential growth formula:
P(t) = P₀ * e^(kt)
where P(t) is the population size at time t, P₀ is the initial population size, k is the growth rate constant, and t is the time elapsed.
In this case, the initial population size P₀ is 5, the final population size P(5) is 160, and the time elapsed t is 5 hours. We want to find the growth rate constant k.
Plugging in the values, we get:
160 = 5 * e^(5k)
Divide by 5:
32 = e^(5k)
Now, take the natural logarithm (ln) of both sides to isolate k:
ln(32) = ln(e^(5k))
Using the property that ln(a^b) = b * ln(a):
ln(32) = 5k * ln(e)
Since ln(e) = 1:
ln(32) = 5k
Now, divide by 5:
k = (ln(32)) / 5 ≈ 0.4641 (rounded to four decimal places)
So, the growth rate constant k is approximately 0.4641 per hour.
To express the rate of growth as a percentage, multiply the growth rate constant by 100:
0.4641 * 100 ≈ 46.41%
The population of yeast cells is growing at a rate of approximately 46.41% per hour.
The rate of growth of the yeast cells is 31 cells per hour.
Explanation:The rate of growth of the yeast cells can be calculated by finding the average rate of change in the population over the given time period.
In this case, the population increased from 5 to 160 in 5 hours, so the average rate of growth can be calculated as (160 - 5) / 5 = 31. The rate of growth of the yeast cells is 31 cells per hour.
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The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).
15,9, 27/5
Find the 10th Term
Therefore , the solution of the given problem of sequence comes out to be the sequence's roughly 10th term is 0.049 (rounded to the closest thousandth).
What is sequence?A sequence is a grouping of range numbers, or "terms." There are phrases like 2, 5, but choose 8. Certain narrative arcs can be made to go on forever by choosing to capitalise on a certain pattern that they exhibit. Use the designs 2, 5, 8, and then 3 to lengthen it. In a list of words for words, there exist formulas that show where to look. In mathematics, a sequence is a group of items that are ordered in some way.
Here,
The first three terms in the given sequence are 15, 9, and 27/5.
We must determine the pattern or rule that underlies the sequence in order to determine the tenth word.
=> 9 = 15 * (27/5) / 15
=> 27/5 = 9 * (27/5) / 9
Thus, each term is obtained by multiplying the constant value by (27/5) / 15, which may be written as 9/25.
In order to get the next phrase in the series, we can keep multiplying the preceding term by 9/25 using this constant value:
=> 9 * (9/25)⁷
When we compute this expression, we obtain:
=> (Rounded to the closest thousandth) 9 * (9/25)⁷
As a result, the sequence's roughly 10th term is 0.049 (rounded to the closest thousandth).
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You may need to use the appropriate technology to answer this question.
The success of an airline depends heavily on its ability to provide a pleasant customer experience. One dimension of customer service on which airlines compete is on-time arrival. The tables below contains a sample of data from delayed flights showing the number of minutes each delayed flight was late for two different airlines, Company A and Company B.
Company A
34 59 43 30 3
32 42 85 30 48
110 50 10 26 70
52 83 78 27 70
27 90 38 52 76
Company B
45 63 42 32 67
104 45 27 38 84
75 46 32 50 64
41 36 33 65 64
(a)
Formulate the hypotheses that can be used to test for a difference between the population mean minutes late for delayed flights by these two airlines. (Let 1 = population mean minutes late for delayed Company A flights and 2 = population mean minutes late for delayed Company B flights.)
H0: 1 − 2 < 0
Ha: 1 − 2 = 0
H0: 1 − 2 ≤ 0
Ha: 1 − 2 > 0
H0: 1 − 2 ≥ 0
Ha: 1 − 2 < 0
H0: 1 − 2 ≠ 0
Ha: 1 − 2 = 0
H0: 1 − 2 = 0
Ha: 1 − 2 ≠ 0
(b)
What is the sample mean number of minutes late for delayed flights for each of these two airlines?
Company A
min
Company B
min
(c)
Calculate the test statistic. (Round your answer to three decimal places.)
What is the p-value? (Round your answer to four decimal places.)
p-value =
Using a 0.05 level of significance, what is your conclusion?
Do not Reject H0. There is statistical evidence that one airline does better than the other in terms of their population mean delay time.
Reject H0. There is statistical evidence that one airline does better than the other in terms of their population mean delay time.
Do not reject H0. There is no statistical evidence that one airline does better than the other in terms of their population mean delay time.
Reject H0. There is no statistical evidence that one airline does better than the other in terms of their population mean delay time.
The answers are: A)H0: μ1 − μ2 = 0; Ha: μ1 − μ2 ≠ 0
(b) Means: Company A___50.6___ min.; Company B___52.75___ min.
c)The t-value is -0.30107., The p-value is 0 .764815.
What is a Hypothesis?A hypothesis is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon
A)H0: μ1 − μ2 = 0
i.e there is no difference between the means of delayed flight for two different airlines
Ha: μ1 − μ2 ≠ 0
i.e there is a difference between the means of delayed flight for two different airlines
(b)
Company A___50.6___ min.
Company B___52.75___ min.
Mean of Company A = x`1= ∑x/n =34+ 59+ 43+ 30+ 3+ 32+ 42+ 85+ 30+ 48+ 110+ 50+ 10+ 26+ 70+ 52+ 83+ 78+ 27+ 70+ 27+ 90+ 38+ 52+ 76/25
= 1265/25= 50.6
Mean of Company B = x`2= ∑x/n =
=46+ 63+ 43+ 33+ 65+ 104+ 45+ 27+ 39+ 84+ 75+ 44+ 34+ 51+ 63+ 42+ 34+ 34+ 65+ 64/20
= 1055/20= 52.75
Difference Scores Calculations
Company A
Sample size for Company A= n1= 25
Degrees of freedom for company A= df1 = n1 - 1 = 25 - 1 = 24
Mean for Company A= x`1= 50.6
Total Squared Difference (x-x`1) for Company A= SS1: 16938
s21 = SS1/(n1 - 1) = 16938/(25-1) = 705.75
Company B
Sample size for Company B= n1= 20
Degrees of freedom for company B= df2 = n2 - 1 = 20 - 1 = 19
Mean for Company B= x`2= 52.75
Total Squared Difference (x-x`2) for Company B= SS2=7427.75
s22 = SS2/(n2 - 1) = 7427.75/(20-1) = 390.93
T-value Calculation
Pooled Variance= Sp²
Sp² = ((df1/(df1 + df2)) * s21) + ((df2/(df2 + df2)) * s22)
Sp²= ((24/43) * 705.75) + ((19/43) * 390.93) = 566.65
s2x`1 = s2p/n1 = 566.65/25 = 22.67
s2x`2 = s2p/n2 = 566.65/20 = 28.33
t = (x`1 - x`2)/√(s2x`1 + s2x`2) = -2.15/√51 = -0.3
The t-value is -0.30107.
The total degrees of freedom is = n1+n2- 2= 25+20-2=43
The critical region for two tailed test at significance level ∝ =0.05 is
t(0.025) (43) = t > ±2.017
Since the calculated value of t= -0.30107. does not fall in the critical region t > ±2.017, null hypothesis is not rejected that is there is no difference between the means of delayed flight for two different airlines.
The p-value is 0 .764815. The result is not significant at p < 0.05.
C) Do not reject H0. There is no statistical evidence that one airline does better than the other in terms of their population mean delay time.
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Write an expression for the total length of the line segments, and simplify it. z z 8 and x x x
None of the given numbers make the equation 8/y² + 2 true
What is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.
To solve this problem, we can substitute each of the given numbers (0, 1, 2, 3, 4) for y in the equation 8/y² + 2 and see if the equation is true.
Substituting y=0 would make the denominator of the fraction zero, which is undefined, so y=0 is not a valid choice.
Substituting y=1 would give us:
8/1² + 2 = 8 + 2 = 10
So, 1 is not the answer.
Substituting y=2 would give us:
8/2² + 2 = 8/4 + 2 = 2 + 2 = 4
So, 2 is not the answer.
Substituting y=3 would give us:
8/3² + 2 = 8/9 + 2 = 0.888 + 2 = 2.888
So, 3 is not the answer.
Substituting y=4 would give us:
8/4² + 2 = 8/16 + 2 = 0.5 + 2 = 2.5
So, 4 is not the answer.
Therefore, none of the given numbers make the equation 8/y² + 2 true.
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the difference of 25 and a number?
Answer: 30 and 5
Step-by-step explanation:
The world record for the heaviest train pulled with a human beard is a 2 3/4 metric tons. How much heavier is the train pulled by teeth than the train pulled with a beard
Answer:
The train pulled by teeth is 1.45 metric tons heavier or 1 9/20 metric tons heavier than the train pulled with a beard.
Step-by-step explanation:
Least Common Denominator (LCD): 20
2 3/4 metric tons = 2 15/20 = 2.75 metric tons
4 1/5 metric tons = 4 4/20 = 4.2 metric tons
FRACTION:
4 4/20 = 84/20
2 15/20 = 55/20
DECIMAL:
4.20-2.75 = 1.45 metric tons
Difference In Weight: (84-55)/20 = 29/20 = 1 9/20 = 1.45 metric tons
4.2/2.75 = 52.727273% heavier
HOPE THIS HELPS!!!
Is 3/5 greater than 3/4
Answer:
no, 3/4 is bigger because 3/5 is cut into more pieces then 3/4
Step-by-step explanation:
find the value of x
Therefore, the height of the right triangle is 9.6 units.
What is triangle?A triangle is a geometric figure that consists of three line segments that intersect at three endpoints, called vertices. The line segments are called sides, and the vertices where they intersect are called angles. A triangle can be classified based on the length of its sides and the measure of its angles. Triangles are fundamental to many areas of mathematics and physics, and they have a wide range of applications in real-life situations, such as in architecture, engineering, and surveying.
Here,
To find the height of a right triangle, we can use the formula:
h = (a * b) / c
where "a" and "b" are the lengths of the legs of the right triangle, and "c" is the length of the hypotenuse.
In this case, we have a right triangle with legs of lengths 12 units and 16 units, and a hypotenuse of length 20 units. Therefore, we can substitute these values into the formula and solve for the height:
h = (12 * 16) / 20
h = 192 / 20
h = 9.6
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I need help with this problem it's is
8x+5+3x+8=90
Answer:
x = 7
Step-by-step explanation:
8x + 5 + 3x + 8 = 90
11x + 5 + 8 = 90
11x + 13 = 90
11x = 77
x = 7
Let's Check
8(7) + 5 + 3(7) + 8 = 90
56 + 5 + 21 + 8 = 90
61 + 21 + 8 = 90
82 + 8 = 90
90 = 90
So, x = 7 is the correct answer!
Answer:
7
Step-by-step explanation:
First, collect common factors. This means put the x's together and the regular numbers together.
8x+3x=11x
5+8=13
11x+13=90
Subtract 13 from both sides
11x+13=90
-13 -13
11x=77
Divide 77 by 11
x=7
Hope this helps! :)
Point B(5,-2) is translated 4 units right and 2 units down and then dilated by a factor of 2 using the origin as the center of dilation what is the resultant point?
the the coordinates of the resulting point are (18, -8). of the resulting point are (18, -8).
What is center of dilation?
The center of dilation is a fixed point in the plane.
Starting with point B(5, -2), if we move it 4 units to the right and 2 units down, we get:
B'(9, -4)
Next, we need to dilate the point by a factor of 2, using the origin as the center of dilation. This means we need to multiply both the x-coordinate and y-coordinate of B' by 2.
So, doubling the x-coordinate of B' gives:
2 × 9 = 18
And doubling the y-coordinate of B' gives:
2 × (-4) = -8
Therefore, the coordinates of the resulting point are (18, -8).
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A diamond merchant received a shipment of 7/10 of a pound of diamonds. He divided the diamonds into 7 equal lots and sold them to jewelers for making rings and necklaces. What was the weight of the diamonds in each lot? Write your answer as a fraction or as a whole or mixed number.
The weight of the diamonds in each lot is 4.9 pounds.
What is the fractional idea?Here, the fractional idea can be used. A fraction represents a portion of a total. A fraction is a numerical figure that designates a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain value, or an object.
A cargo of half a pound's worth of diamonds was received by a diamond trader. He separated the stones into 4 equal lots and sold them to jewelers so they could be used to make necklaces and rings.
Total shipment = 7/10 pound
number of equal lots = 7
then, 7 x weight = 7/10
weight = 4.9
Therefore, the weight of each lot is 4.9 pounds.
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1/2 of 50 of 1/4 of ?
Answer:
[tex] \frac{1}{2} \times 50 \times \frac{1}{4} = 50 \times \frac{1}{8} = \frac{25}{4} = 6 \frac{1}{4} [/tex]
Find ordered pairs y=-7x+8
The ordered pairs for the equation y = -7x + 8 are (0, 8), (1, 1), and (-1, 15).
What are the ordered pairs for the equation y?To find ordered pairs for the equation y = -7x + 8, we can substitute different values of x and solve for y.
Let's choose three values of x:
When x = 0, y = -7(0) + 8 = 8. So one ordered pair is (0, 8).
When x = 1, y = -7(1) + 8 = 1. So another ordered pair is (1, 1).
When x = -1, y = -7(-1) + 8 = 15. So another ordered pair is (-1, 15).
Therefore, the ordered pairs are (0, 8), (1, 1), and (-1, 15).
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A certain virus infects one in every 300 people. A test used to detect the virus in a person is positive 85% of the time if the person has the virus and 10% of the time if the person does not have the virus. (This 10% result is called a false positive.) Let A be the event "the person is infected" and B be the event "the person tests positive".
The probability that a person has the virus given that they have tested positive is 3.24%.
The probability that a person does not have the virus given that they test negative is 99.93%.
What is Probability?Here we have following probabilties:
P(A)=1/300, P(A')=1-(1/300)=299/300
P(B|A)=0.80, P(B|A')= 0.08
From the law of total probability is
P(B)=P(B|A)P(A)+P(B|A')P(A')
[tex]=0.80\cdot \frac{1}{300}+0.08\cdot \frac{299}{300}\\\\=0.0824[/tex]
By the Baye's theorem we have
P(A|B) = [tex]\frac{P(B|A)P(A)}{P(B)}\\\\=\frac{0.80\cdot \frac{1}{300}}{0.0824}\\\\=0.0324[/tex]
So the probability that a person has the virus given that they have tested positive is 3.24%.
(b)
From the law of total probability is
P(B')=P(B'|A)P(A)+P(B'|A')P(A')
[tex]=0.20\cdot \frac{1}{300}+0.92\cdot \frac{299}{300}\\\\=0.9176[/tex]
By the Baye's theorem we have
P(A'|B')=[tex]\frac{P(B'|A')P(A')}{P(B')}\\\\=\frac{0.92\cdot \frac{299}{300}}{0.9176}\\\\=0.9993[/tex]
So the probability that a person does not have the virus given that they test negative is 99.93%.
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can anyone explain how to solve this
Mortgage (monthly)
Amount
$985.64
Cell phone (monthly)
$58.30
Groceries (twice a month
$154.00
Clothing (monthly with 25% job-related) $180.00
Water & electric (monthly)
S128.40
Weekly dinner & movie
$55.00
Property taxes (6 months)
$684.80
Car insurance (guarterly)
$330.00
Your realized income is $2.943.20/month. How much are your fixed expenses each month? How much could you save per month if you take 25% of your discretionary monies and put it in a savings account?
Answer:
To calculate the fixed expenses each month, we need to add up all the monthly expenses:
Mortgage: $985.64
Cell phone: $58.30
Groceries: $154.00 x 2 = $308.00
Clothing (with 25% job-related): $180.00
Water & electric: $128.40
Weekly dinner & movie: $55.00 x 4 = $220.00
Total monthly fixed expenses: $1,880.34
To calculate how much could be saved per month, we need to first calculate the discretionary income:
Realized income: $2,943.20
Fixed expenses: $1,880.34
Discretionary income: $2,943.20 - $1,880.34 = $1,062.86
25% of discretionary income: 0.25 x $1,062.86 = $265.72
Therefore, the amount that could be saved per month by putting 25% of the discretionary income in a savings account is $265.72.
What is the area of the parallelogram shown below?
17
8
units2
9
17
4
======================================================
Explanation:
The triangle on the left has a = 8 as one of the legs, and c = 17 as the hypotenuse. Use the pythagorean theorem to find the missing side.
[tex]a^2+b^2 = c^2\\\\8^2+b^2 = 17^2\\\\64 + b^2 = 289\\\\b^2 = 289-64\\\\b^2 = 225\\\\b = \sqrt{225}\\\\b = 15\\\\[/tex]
This is the height of the parallelogram as marked by the dashed line.
The base is 9 units across the bottom. We won't use 8 as the base because it's too short along the top.
area = base*height
area = 9*15
area = 135 square units
For each of the following three scenarios, state which hypothesis test you would use from among the four introduced so far: the z test, the single-sample t test, the paired-samples t test, and the independent-samples t test. (Note: In the actual studies described, the researchers did not always use one of these tests, often because the actual experiment had additional variables.) Explain your answer. (20pts) a. A study of 40 children who had survived a brain tumor revealed that the children were more likely to have behavioral and emotional difficulties than were children who had not experienced such a trauma (Upton & Eiser, 2006). Parents rated children’s difficulties, and the ratings data were compared with known means from published population norms. b. Talarico and Rubin (2003) recorded the memories of 54 students just after the terrorist attacks in the United States on September 11, 2001—some memories related to the terrorist attacks on that day (called flashbulb memoriesfor their vividness and emotional content) and some everyday memories. They found that flashbulb memories were no more consistent over time than everyday memories, even though they were perceived to be more accurate. c. The HOPE VI Panel Study (Popkin & Woodley, 2002) was initiated to test a U.S. program aimed at improving troubled public housing developments. Residents of five HOPE VI developments were examined at the beginning of the study so researchers could later ascertain whether their quality of life had improved. Means at the beginning of the study were compared to known national data sources (e.g., the U.S. Census, the American Housing Survey) that had summary statistics, including means and standard deviations.
Answer:
a. For the study of 40 children who had survived a brain tumor, the appropriate hypothesis test would be a single-sample t test. This is because the study involves comparing the ratings data from the parents with known means from published population norms. A single-sample t test is used to determine whether a sample mean is statistically different from a known population mean. In this case, the sample mean is the ratings data from the parents, and the population mean is the known means from published population norms.
b. For Talarico and Rubin's study of memories, the appropriate hypothesis test would be a paired-samples t test. This is because the study involves comparing the consistency of flashbulb memories and everyday memories over time, for the same group of individuals. A paired-samples t test is used to determine whether there is a statistically significant difference between two related samples, such as before and after measurements for the same group of individuals.
c. For the HOPE VI Panel Study, the appropriate hypothesis test would be an independent-samples t test. This is because the study involves comparing the means of residents in the five HOPE VI developments at the beginning of the study with known national data sources that had summary statistics, including means and standard deviations. An independent-samples t test is used to determine whether there is a statistically significant difference between the means of two independent groups. In this case, the two independent groups are the residents in the HOPE VI developments and the known national data sources.
Step-by-step explanation:
You take out a loan in the amount of your tuition and fees cost $70,000. The loan has a monthly interest rate of 0.25% and a monthly payment of $250. How long will it take you to pay off the loan? Use the formula N= (-log(1-i*A/P))/(log(1+i)) to determine the number of months it will take you to pay off the loan. Let N represent the number of monthly payments that will need to be made, i represent the interest rate in decimal form, A represent the amount owed (total amount of the loan), and P represent the amount of your monthly payment. Be sure to show your work for all calculations made.
It will take 4.645 months to pay off the loan, which rounds up to 5 months.
Define interest rateInterest rate is the percentage of the principal amount charged by a lender or creditor for the use of borrowed money. In other words, it is the cost of borrowing money, usually expressed as an annual percentage rate (APR) or as a periodic rate for a specific time period.
Given:
Total amount of the loan (A) = $70,000
Monthly interest rate (i) = 0.25% = 0.0025
Monthly payment (P) = $250
We need to find the number of monthly payments (N) needed to pay off the loan.
Using the given formula:
N = (-log(1 - i×A/P))/(log(1+i))
Substituting the values we get:
N = (-㏑(1 - 0.0025×70000/250))/(log(1+0.0025))
N = (-㏑(0.72))/(㏑1.0025))
N = (-(-0.337))-4.308
N = 4.645 (approx.)
Therefore, it will take approximately 4.645 months to pay off the loan, which rounds up to 5 months.
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F(x)=2/3x-1 show creat points to graph
Label values on thex&y axis
To create points for the graph of f(x) = (2/3)x - 1, we can choose values of x and calculate the corresponding values of f(x). See explanation below and attached graph.
What is the explanation for the above response?To create points for the graph of f(x) = (2/3)x - 1, we can choose values of x and calculate the corresponding values of f(x). For example:
When x = -3, f(x) = (2/3)(-3) - 1 = -3 - 1 = -4When x = -2, f(x) = (2/3)(-2) - 1 = -2 1/3When x = -1, f(x) = (2/3)(-1) - 1 = -1 2/3When x = 0, f(x) = (2/3)(0) - 1 = -1When x = 1, f(x) = (2/3)(1) - 1 = -1/3When x = 2, f(x) = (2/3)(2) - 1 = 1/3When x = 3, f(x) = (2/3)(3) - 1 = 1So, we have the following points for the graph: (-3, -4), (-2, -2 1/3), (-1, -1 2/3), (0, -1), (1, -1/3), (2, 1/3), (3, 1).
We can now plot these points on a graph, with x-values on the horizontal axis and f(x) values on the vertical axis. We can label the horizontal axis as "x" and the vertical axis as "f(x)" or "y".
Note that the graph of f(x) = (2/3)x - 1 is a straight line with slope 2/3 and y-intercept -1.
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$1000 is deposited in an account with a
8.5% interest rate, compounded
continuously.
What is the balance after 5 years?
P = $1000 r = 0.085 t = 5
F = Pet F = $[?]
Round to the nearest cent.
Answer:
$1529.59
Step-by-step explanation:
You want the balance in an account earning 8.5% interest compounded continuously for 5 years if the initial balance was $1000.
Continuous compoundingThe formula for the account balance is given as ...
F = P·e^(rt)
F = 1000·e^(0.085·5) ≈ 1529.59
The balance after 5 years is $1529.59.
<95141404393>
secQ=
2√6
Q
9
Help answer!!
Answer: the simplified form of sec(Q) is sqrt(24/7).
Step-by-step explanation: The equation secant of angle Q is equal to two multiplied by the square root of six and divided by nine.
In order to reduce the complexity of the given mathematical expression, it is possible to employ the fundamental definition of secant, which states that:
The trigonometric identity denoted as sec(Q) equals the reciprocal of the cosine function evaluated at the angle Q. More precisely, sec(Q) = 1 / cos(Q).
The value of cos(Q) may be determined through the utilization of the Pythagorean identity.
The present mathematical equation demonstrates a fundamental identity in trigonometry, wherein the squares of the sine and cosine functions are summed to equal one. Written symbolically, the equation can be expressed as sin^2(Q) + cos^2(Q) = 1.
Given the condition that sec(Q) is positive, it is ascertainable that Q is situated within the first or fourth quadrant, wherein the cosine of Q is likewise positive. Consequently, the derivation for the solution of the cosine of the angle Q can be expressed as follows:
The trigonometric identity expressed as cos(Q) = sqrt(1 - sin^2(Q)) is a fundamental result in the field of mathematics. This particular equation provides a relationship between the cosine and sine functions of angle Q. Specifically, it states that the cosine of an angle Q is equal to the square root of one minus the sine squared of the same angle Q. The use of such identities is common in mathematical analysis and applied sciences, where it allows for efficient manipulation of trigonometric functions and the mathematical modeling of a variety of physical phenomena.
The following mathematical expression can be written in an academic style: Cosine of angle Q can be expressed as the square root of one minus the square of nine divided by twice the square root of six, i.e., cos(Q) = √(1 - (9/2√6)^2), while substituting the value of sine of angle Q as being equal to nine divided by twice the square root of six (i.e., sin(Q) = 9/2√6).
The mathematical expression cos(Q) = sqrt(1 - (81/24)) may be represented in a more academic manner. Specifically, it may be articulated as follows: the cosine of angle Q is equivalent to the square root of one subtracted by the quotient of 81 and 24. This revision lends itself to a more formal and precise mode of communication, which is characteristic of academic writing.
The mathematical expression cos(Q) = √(7/24) can be represented in a formal and academic manner.
The value of secant of angle Q can now be determined as:
The trigonometric function defining the secant of an angle Q is expressed as sec(Q) = 1/cos(Q).
The trigonometric function, sec(Q), can be expressed as the reciprocal of the square root of 7/24.
The mathematical statement, sec(Q) = sqrt(24/7), can be expressed in a formal and academic manner as follows. The reciprocal of the cosine function of the angle Q is equivalent to the square root of the fraction 24 over 7.
Find the deductions and the net pay. Social Security is 6.2 percent of the first $90,000. Medicare is 1.45 percent of all income. $90,000. For Problems 3-7, the state tax is 2 percent of gross pay and the local tax is 1.5 percent of gross pay.
The minimum value of Jeri Dammers' total deductions is $200.68.
What is the deductions?Based on the given information, we can calculate the total deductions for Jeri Dammers as follows:
Social Security: Jeri pays 6% of the first S$90,000 of her gross pay towards Social Security. As her gross pay is only $735.00, her Social Security deduction will be:
Social Security = 6% of $735.00 = $44.10Medicare: Jeri pays 1.45% of all her income towards Medicare. As her gross pay is $735.00, her Medicare deduction will be:
Medicare = 1.45% of $735.00 = $10.65Federal Income Tax: To calculate the federal income tax, we need to refer to the tax tables provided by the IRS. As the gross pay is only $735.00, Jeri's federal income tax deduction will be very minimal or possibly none.
State Tax: Jeri pays 2% of her gross pay towards state tax. As her gross pay is $735.00, her state tax deduction will be:
State = 2% of $735.00 = $14.70Local Tax: Jeri pays 1.5% of her gross pay towards local tax. As her gross pay is $735.00, her local tax deduction will be:
Local = 1.5% of $735.00 = $11.03Medical: Jeri has a deduction of $32.00 towards medical expenses.
Union Dues and Others: No information is given about Jeri's union dues or other deductions.
Therefore, the total deductions for Jeri Dammers will be:
Total Deductions = Social Security + Medicare + Federal Income Tax + State Tax + Local Tax + Medical + Union Dues + OthersTotal Deductions = $44.10 + $10.65 + $0 + $14.70 + $11.03 + $32.00 + Union Dues + OthersTotal Deductions = $112.48 + Union Dues + OthersWe cannot calculate the exact value of Total Deductions without information about Union Dues and Others.
However, the minimum value of Total Deductions would be:
Total Deductions (minimum)= $44.10 + $10.65 + $88.20 + $14.70 + $11.03 + $32.00
= $200.68
Therefore, the minimum value of Jeri Dammers' total deductions is $200.68.
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See full text below
Find the total deduction The person pays Social Security 6 percent of the first S90,000. Medicare is 1.45 percent of all income Use the tax tables for federal tax The state tax is 2 percent of gross pay and the local tax is 1.5 percent of gross pay. (Remember to add the Medical; Union Dues, and Others for total deduction: FIT Federal Income Tax, FICA Social Security) .4. Jeri Dammers is married and claims 3 allowances.
Dept
Employee
Check Number -3205
Gross Pay -$735.00
Net Pay
44B Jeri Dammers
Tax Deductions
Other Deductions
FIT
FICA
Medicare
State
Local
Medical -32.00
Union
Dues
Others
If 4 < a < 5 and 2 < b < 4, find all possible values for each expression:
-2a + 3b
The potential values for the equation -2a + 3b, for given inequalities 4 < a < 5 and 2 < b < 4 are: (-8 + 3b), (-10 + 3b), (-2a + 6), and (-2a + 12), where 'a' and 'b' can take any value within their respective provided ranges.
What is "Inequalities" in mathematics?In mathematics, inequalities are mathematical expressions or statements that compare the relative magnitude of two or more numbers or quantities. They are used to depict connections such as "greater than," "less than," "greater than or equal to," "less than or equal to," and "not equal to" between numbers or mathematical expressions.
Some generally known types of inequalities in mathematics are:
Linear inequalitiesQuadratic inequalitiesRational inequalitiesExponential inequalities etc.For given problem,
Given that 4 < a < 5 and 2 < b < 4, we can consider the extreme values of 'a' and 'b' within these ranges to find the possible values of the expression.
When 'a' is at its Minimum, it equals 4: -2a + 3b = -2(4) + 3b = -8 + 3bWhen 'a' is at its Maximum, it equals 5:-2a + 3b = -2(5) + 3b = -10 + 3bWhen 'b' is at its Minimum, it equals 2:-2a + 3b = -2a + 3(2) = -2a + 6When 'b' is at its Maximum, it equals 4:-2a + 3b = -2a + 3(4) = -2a + 12So, the four potential values for the expression -2a + 3b, where 4 < a < 5 and 2 < b < 4, are:
-8 + 3b, -10 + 3b, -2a + 6, and -2a + 12
where 'a' and 'b' can take any value within their respective given ranges.
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Answer: -4 and 4
Step-by-step explanation:
use the lowest value for a and the highest for b
Find any solution(s) (refer to attachment) of and select the correct statement.
A. The equation has no solution.
B. The equation has two solutions.
C. The equation has one solution.
D. The equation has one solution and one extraneous solution.
