The value of the larger number and the smaller number are 25 and 8 respectively.
What is Simultaneous Equation?Simultaneous equations are two or more algebraic equations that share variables e.g. x and y.
They are called simultaneous equations because the equations are solved at the same time.
If the bigger value is represented by x and the smaller value is represented by then
x+y= 33 equation 1
3x+ 4y= 107 equation 2
using Elimination method,
we multiply the coefficients of x by opposite equation
3x+3y=99 equation 3
3x+4y= 107 equation4
subtracting equation 3 from 4
y=107- 99
y= 8
substituting 8 for y in equation 1
x+8= 33
x= 33-8=25
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Use the properties of congruent triangle to find the value of x and y. Be sure to show all your work
Answer:Angles in a triangle may or may not be congruent.
The values of x and y are 90 and 47, respectively.
From the figure, we have:
This means that, angle x is a right-angle.
So, we have:
Triangle ABC is an isosceles triangle.
So, we have:
The measure of y is then calculated as:
--- sum of angles in a triangle
This gives
Subtract 137 from both sides
Hence, the values of x and y are 90 and 47, respectively.
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Step-by-step explanation:
Question
Find the rate if a principal of $1,100 earned $1,089 interest in 12
years.
Answer:
Step-by-step explanation:
Intrest = PRT\100
$1089. =. ($1100x12xR)\100
$1089. = 132R
Divide through by 132.
R. =. 8.25%
How is Addy 4+ -4 similar to adding 4+4 how is it different use the words and models to explain
4- (+) (-4) is similar to 4+4 by the rule of addition in integers that is if Negative + Negative then Add the number and put the sign of greater number.
What is integer?Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the corresponding positive numbers are the negative numbers. An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples. Three categories of integers exist: Zero (0) (0) Good integers (Natural numbers) Integer Negatives (Additive inverse of Natural Numbers).
The rules of addition in integers says,
- + - = +
by this,
4-(-4)=8
by concept of addition,
4+4=8
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If A = (1 , 4) and B = ( 7 , 6), then coordinates of the midpoint of AB are
Answer:
(4 , 5)
Step-by-step explanation:
midpoint formula: (x1+x2/2 , y1+y2/2)
so
(1+7/2 , 4+6/2)
(8/2 , 10/2)
4 , 5
An orange grove manager uses two different sized buckets to load oranges into a truck. The first bucket can transport a pound of oranges, and the second bucket can transport
y pounds of oranges. The first bucket is filled up G times and the second bucket is filled up I times The total amount of oranges. I that have been loaded can be found usina
the equation T = Ga + Hy.
Solve for H.
T + Ge
O H
y
O H= y(T - Gx)
T
0 H = Gx+y
T_ Cr
O H
2
On solving for [H], we get -
H = (T - Ga)/y
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have the following equation -
T = Ga + Hy
We have -
T = Ga + Hy
Solving for [H], we get -
Hy = T - Ga
H = (T - Ga)/y
Therefore, On solving for [H], we get -
H = (T - Ga)/y
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In your own words, describe the y-intercept.
Answer:
The y-intercept is the point where the graph ( line or curve ) intercepts the y-axis. The y-intercept is the y value of the point, ( x, y ).
Hope this helps!
Step-by-step explanation:
Question 3 of 10
The blue segment below is a diameter of 0. What is the length of the radius
of the circle?
7.7
0
A. 15.4 units
B. 3.85 units
C. 11.55 units
D. 7.7 units
Answer:
I think B. 3.85 units
Step-by-step explanation:
Calculate the number of different three-course meals a patron could choose from at the Butcher Shop Steakhouse during Restaurant Week. What conditions had to be met for you to calculate the number of different outcomes for this experiment?
The probability of getting watermelon is 3/58.
The given values are
A pineapple chew was selected 53 Times
A lemon chew was selected 2 times
A watermelon chew was selected 3 times
The probability that you Bella remove from the bag is pineapple chew.
probability is which we can't predict actual it is usually about the prediction
As we know
probability - expected outcome/total outcome
The question Bela perform experiment 58 times then the total outcome will be 58 if you pineapple was selected 53 times the probability of the chew Bella pick of pineapple is 53/58
The probability of Bella pick chew of lemon -2/58
The probability of Bella pick watermelon is - 3/58
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tenths hundreths thousands
1. 67.925
2. 182.0051
3. 39.1432
4. 85. 0267
5. 97.7352
Answer:
Step-by-step explanation:
1) sixty-seventh and nine hundred and twenty-five thousands
2)one-eighty two and fifty-one thousands
3)thirty-nine and thousand four thirty two thousands
4) eighty five and two sixty seven thousands
5) ninety seven and seven thousand and three-fifty two thousands
Write an exponential function in the form y = ab^x that goes through points (0, 14)
and (4,8750).
The exponential function will be written as y = 14⁰.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given exponential function is [tex]y = ab^x[/tex]. The equation of the exponential function passing through the point is,
[tex]y = ab^x \\[/tex]
14 = ab⁰
a = 14
The equation will be written as,
y = 14b⁰
y = 14⁰
Therefore, the exponential function will be written as y = 14⁰.
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The diagram shows a triangle. Complete parts a and b below. (4 points)
53⁰
8p+10°
2p+17°
A- write an equation and solve for p. Show all work.
B-List the measures of the three angles.
The value of p is 10 and the angles of the triangles are 53°, 90°, 37°.
Given that,
In the picture there is a triangle with angles 53°, 8p+10°, 2p+17°.
We have to find the p value and each of the angles also.
What is angles in triangles?While the exterior angles of a triangle are equal to the sum of the two interior angles that are not adjacent to it, the interior angles of a triangle always add up to 180°. By deducting the angle of the target vertex from 180°, one can also determine a triangle's exterior angle.
Take the angles ,
180 degrees is the sum of the angles in an triangle.
53°+ 8p+10°+ 2p+17°=180°
10p+80°=180°
10p=180°-80°
10p=100°
p=100/10
p=10°
The value of p=10.
The angles of the triangles are:
53°
8p+10=8(10)+10=80+10=90°
2p+17=2(10)+17=20+17=37°
Therefore, The value of p is 10 and the angles of the triangles are 53°, 90°, 37°.
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Suppose a large shipment of stereos contained 18% defectives. If a sample of size 306 is selected, what is the probability that the sample proportion will differ from the population proportion by more than 6%? Round your answer to four decimal places.
The probability that the sample proportion of a large shipment of stereos will differ from the population proportion by more than 6% is 0.0063
How to get the required probabilityThe probability is calculated using z score, this is used to determine the amount of standard deviations a sample, X is from the mean
The z score is given by the formula
z = (X - μ) / σ
Definition of variables
mean, μ = p = 18% = 0.18
sample size, n = 306
standard deviation, σ
= √{(p(1 - p)) / n}
= √{(0.18(1 - 0.18)) / 306}
= √{(0.18 * 0.82) / 306}
= 0.02196
The probability
differ from the population proportion by less than 3%
|X - 0.18| > 0.06
X < 0.12 OR X > 0.24
P(z < 0.12) + P(z > 0.24 )
z score for z < 0.06
z = (0.12 - 0.18) / 0.02196
= -2.7322
p value for z < -2.7322 = 0.003146
z score for z > 0.06
z = (0.24 - 0.18) / 0.02196
= 2.7322
p value for z > 2.7322 = 1 - 0.99685 = 0.003146
The probability required = 0.003146 + 0.003146 = 0.006292 = 0.63%
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The mean systolic blood pressure of people in the U.S. is
124
124 with a standard deviation of
18
18. Assume that systolic blood pressure follows a normal distribution. Round your answers to one decimal. Use the 68-95-99.7 Rule to answer the following questions.
a) What percentage of the people in the U.S. have systolic blood pressure between
106
106 and
124
124?
%
%
Preview
b) What percentage of the people in the U.S. have systolic blood pressure between
88
88 and
160
160?
%
%
Preview
c) What percentage of the people in the U.S. have systolic blood pressure between
70
70 and
124
124?
%
%
Preview
d) What percentage of the people in the U.S. have systolic blood pressure above
160
160?
%
%
The percentages, using the Empirical Rule, are given as follows:
a) Between 106 and 124: 32%.
b) Between 88 and 160: 95%.
c) Between 70 and 124: 49.85%.
d) Above 160: 2.5%.
What does the Empirical Rule state?The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:
The percentage of scores within one standard deviation of the mean of the distribution is of approximately 68%.The percentage of scores within two standard deviations of the mean of the distribution is of approximately 95%.The percentage of scores within three standard deviations of the mean off the distribution is of approximately 99.7%.The mean and the standard deviation in this problem are given as follows:
Mean of 124.Standard deviation of 18.Considering the symmetry of the normal distribution, to facilitate the calculations, we have that:
49.85% of the measures are between 70 and 124.47.5% of the measures are between 88 and 124.32% of the measures are between 106 and 124.32% of the measures are between 106 and 142.47.5% of the measures are between 124 and 160.49.85% of the measures are between 124 and 178.160 is two standard deviations above the mean, hence the percentage above it is of:
2.5%.
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Two year ago ernest dorsey purchased a used sports coupe for 8000.00 that is now worth 6000.00 last year he drove it 13569 miles and kept a record od all expenses. His variable costs were gasoline $1589.56 oil changes $245.98 and repairs $548.11 his fix costs were insurance $1105.32 and license $85 find de cost per mile
The cost per mile incurred by Ernest Dorsey for driving the sports coupe for last year was $0.41.
How is the cost per mile derived?The cost per mile is the quotient of the division operation involving the total cost incurred and the driving mileage for the year.
To derive the total cost, add up the value of the car consumed (cost - current value), the annual variable, and fixed costs.
Cost of a used sports coupe last year = $8,000
The current value of the car = $6,000
Used value for the year = $2,000.00 ($8,000 - $2,000)
Yearly variable costs:Gasoline $1,589.56
Oil changes $245.98
Repairs $548.11 $2,383.65
Annual fixed Costs:Insurance $1,105.32
License $85.00 $1,190.32
Total cost for the year = $5,573.97
Driven mileage for the year = 13,569 miles
Cost per mile = $0.41 ($5,573.97/13,569)
Thus, the cost per mile is $0.41.
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-1/4-a-4=7/4a-3
solving equations with one unlike equations
Answer:
a = -5/11
Step-by-step explanation:
You want to solve the equation -1/4-a-4=7/4a-3.
SolutionThe first step in solving this 3-step equation can be to add the opposite of (-a) so that the variable 'a' appears only on one side of the equation:
-1/4 -a -4 +a = 7/4a -3 +a
-17/4 = 11/4a -3 . . . . . . . . . . . simplify
The second step is to add the opposite of the constant (-3) so that the constant is on one side of the equation, and the variable is on the other side.
-17/4 +3 = 11/4a -3 +3
-5/4 = 11/4a . . . . . . . . . . simplify
The third step is to multiply by the inverse of the coefficient of the variable:
(4/11)(-5/4) = (4/11)(11/4a)
-5/11 = a . . . . . . . . . . . . . . . simplify
Check-1/4 -(-5/11) -4 = (7/4)(-5/11) -3
-17/4 +5/11 = -35/44 -3
(-187 +20)/44 = (-132 -35)/44
-167/44 = -167/44 . . . . . . answer checks OK
Daniel has invested $300 in an annuity each month, earning 4% interest for 20 years.
Sarah has invested $150 in an annuity each month, earning 4% interest for 40 years.
Which of the following must be true?
Answer: daniel and sarah will deposit the same amount
Consider the function graphed at right.
The function has a maximum
of 3
The function is increasing on the interval(s):
The function is decreasing on the interval(s):
at x =
-4
4
-32
-5--
3 4 5
1 2 3 4 5
Answer:
heyyyyyyyyyyyyyyyyyyyyyyyy
solve 4x + 2=(1/8)x-2
Answer:
x = -32/31
Step-by-step explanation:
4x - 1/8 x = -2 -2
(32 - 1)/8 x = -4
31/8 x = -4
x = -4 * 8/31
x = -32/31
lee has seven 5-dollar bills and 6 quarters
in his pocket. How much money would he have
left in his pocket if he buys a leather jacket
worth $35.20.
Answer:
Lee would have $1.30 left.
Step-by-step explanation:
7 x 5 = $35
6 x .25 = $1.50
Altogether, Lee has $36.50 before buying the jacket
$36.50 - 35.20 = $1.30
NO LINKS!! Please help me with these graphs Part 2a
Answer:
Left graph.
Domain: all real numbers.
Range: y ≤ 4
Middle graph.
Domain: all real numbers
Range: y ≥ 3
Right graph.
Domain: x ≥ -2
Range: y ≥ -3
Answer:
1. Domain: (-∞, ∞) Range: (-∞, 4]
2. Domain: (-∞, ∞) Range: [3, ∞)
3. Domain: [-2, ∞) Range: [-3, ∞)
Step-by-step explanation:
Definitions
Domain: The set of all possible input values (x-values).Range: The set of all possible output values (y-values).Open circle: The value is not included in the interval.Closed circle: The value is included in the interval.Arrow: The function continues indefinitely in that direction.Note: Assume that each square on the given graphs is 1 unit.
Question 1As there are arrows at both endpoints of the curve, the domain of the function is unrestricted.
Domain: (-∞, ∞)The curve has a maximum point at (2, 4) and continues indefinitely towards negative infinity at both endpoints.
Therefore, the range of the function is restricted.
Range: (-∞, 4]Question 2As there are arrows at both endpoints of the function, the domain is unrestricted.
Domain: (-∞, ∞)The function has a minimum point at y = 3.
When x > -2, the line continues indefinitely at y = 3.
When x < -2, the line continues indefinitely towards infinity.
Therefore, the range of the function is restricted.
Range: [3, ∞)Question 3The domain of the function is restricted since there is a closed circle at one endpoint: (-2, -3). When x > -2, the line continues indefinitely towards infinity.
Domain: [-2, ∞)The function has a minimum point at (-2, -3). As x continues towards infinity, so does y.
Therefore, the range of the function is restricted.
Range: [-3, ∞)What is the b-value?
Answer:
3
Step-by-step explanation:
y-intercept = b
The slope-intercept = y=mx+b
y=-2/5x+3
m=-2/5
b=3
If the equation was something like y=-2x-3, then the b would be -3 because you are subtracting 3.
Is 4.5 greater, less than, or equal to 4 and 1/2
Answer:
equal to
Step-by-step explanation:
4 + 1/2= 4+ 0.5= 4.5
4.5=4.5
20. In Problem 14 in Chapter 11, we described a study
showing that students are likely to improve their test
scores if they go back and change answers after
reconsidering some of the questions on the exam
(Johnston, 1975). In the study, one group of students
was encouraged to reconsider each question and
to change answers whenever they felt it was appropri-
ate. The students were asked to record their original
answers as well as the changes. For each student, the
exam was graded based on the original answers and on
the changed answers. For a group of n = 40 students,
suppose that 26 had higher scores for the changed-
answer version and only 14 had higher scores for
the original-answer version. Is this result significantly
different from chance? Use a two-tailed test with
α = .01.
Find the Average Rate of Change (AROC) of y = 4(1/2)^x over the interval [-2, 0].
a) 6
b) -6
c) 4
d) -4
Answer:
b) -6------------------------
Find the value of the function at the endpoints of the given intervalx = - 2 ⇒ y = 4(1/2)⁻² = 4(2)² = 4(4) = 16x = 0 ⇒ y = 4(1/2)⁰ = 4(1) = 4Average rate of change isChange in y / change in x =(4 - 16)/(0 - (-2)) = - 12 / 2 = - 6Correct choice is B.
Answer:
b) -6
Step-by-step explanation:
The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
Given the interval is [-2, 0]:
a = -2b = 0Substitute the endpoints of the interval into the function and solve:
[tex]\begin{aligned}x=-2 \implies f(-2)&=4\left(\dfrac{1}{2}\right)^{-2}\\& = 4(4)\\&=16\end{aligned}[/tex]
[tex]\begin{aligned}x=0 \implies f(0)&=4\left(\dfrac{1}{2}\right)^{0}\\& = 4(1)\\&=4\end{aligned}[/tex]
Therefore:
[tex]\begin{aligned}\implies\dfrac{f(b)-f(a)}{b-a}&=\dfrac{f(0)-f(-2)}{0-(-2)}\\\\&=\dfrac{4-16}{0+2}\\\\&=\dfrac{-12}{2}\\\\&=-6\end{aligned}[/tex]
PLEASE HELP AND FAST
Answer:
d [tex]\frac{-4}{3}[/tex]
Step-by-step explanation:
change in y over the change in x
[tex]\frac{-2-2}{1- -2}[/tex] = [tex]\frac{-4}{3}[/tex]
mathhhhhhhhhhhhhhhhhhhh
Answer: x = 4. This solution relates to the original equation because when you substitute x for 4, the equation will simplify correctly as 0 = 0.
Step-by-step explanation:
To solve, we will isolate the variable with inverse operations.
Given:
3x - 12 = 0
Add 12 to both sides of the equation:
(3x - 12) + 12 = (0) + 12
3x = 12
Divide both sides of the equation by 3.
(3x) / 3 = (12) / 3
x = 4
This solution, x = 4, relates to the original equation because when you substitute x for 4, the equation will simplify correctly as 0 = 0.
Answer:
x=4
Step-by-step explanation:
3x-12 = 0
Solve the equation
Add 12 to each side using the addition property of equality
3x-12+12 = 0+12
3x= 12
Divide each side by 3 using the division property of equality
3x/3 = 12/3
x = 4
The solution is what satisfies the original equation
The effect of the time of day a science class is laught on test scores is being studied in an experiment. Giving every student in the experiment the same final exam is an example of which experimental design principle?
Giving every student in the experiment the same final exam is an example of A. Randomization.
What is an experimental design?The process of conducting research in an objective and controlled manner in order to maximize precision and draw specific conclusions about a hypothesis statement is known as experimental design.
The process in which participants in clinical trials are randomly assigned to separate groups that receive different treatments or other interventions. Neither the researcher nor the participant has any say in which treatment or intervention the participant receives.
A random process is a sequence of random variables that describe a process whose outcomes follow an evolution described by probability distributions. This was illustrated in the examination.
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Complete options
A. Randomization
B. Blocking
C. Direct control
D. Replication
I had 35 assignments for the week. The ratio for English assignments to the rest of the assignments was 2:3. How many assignments were NOT English?
Answer:
21 Assignments were NOT English.
A number line going from negative 20 to positive 20.
What is the absolute value of –20?
Use the number line to answer the question.
–20
0
20
40
Answer:
20
Step-by-step explanation:
Absolute value is the distance from zero. Absolute value is always positive.
| -20 | is positive. It is 20 units from 0. So it is 20.
| -20 | = 20
(Be careful, absolute value doesn't just flip the sign to the opposite.
| 20 | = 20 also because the distance from 0 to 20 is also 20.)
Fill in the table using this function rule. y=-2x-3
Answer:
6
Step-by-step explanation:
the answer is 6
