Answer:
The interest after one year is $45
Explanation:
Principal = $900
Rate = 5%
Time = 1 year
I = P x R x T / 100
I = 900 x 5 x 1 / 100
I = 4500/100
I = $45
Therefore, the interest after one year is $45
The store clerk put b bottles of milk in the cooler, and 11 of the bottles are chocolate milk.
Choose the expression that shows the number of milk bottles that are not chocolate.
11
b- 11
b + 11
11b
Answer: b-11
Step-by-step explanation:
b= total number of milk
11= total number of chocolate milk
b - 11 = number of milks that aren't chocolate
Rotate point A(3,5) 270° counterclockwise around the origin
the given point is A(3,5)
when we rotate a point (x,y) around origin counterclockwise then its coordinates becomes (y,-x)
so point A(3,5) will be changed into A'(5,-3).
so new coordinate of the point will be A'(5,-3)
Write the equation of line in slope-intercept form, which is parallel to y=−2x+5 and passing through the point (1, −4).
Answer: y= -2x -2
Step-by-step explanation:
1) Create an equation going through (1,-4)
Replace 5 with b otherwise, we can't find an equation that goes through it.
y = -2x + b
2) Substitute y and x with the point. Solve.
-4 = -2(1) + b
-4 = -2 + b
-2 = b
3) Reput in the equation
y= -2x -2
Note: It is parallel because they have the same slope!
what amount of time in months is necessary for a principal of $6,000 to produce $550 and interest at 10%?
the compound interest formula is given by
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where A is the amount you will have, P is the principal, r is the annual interest rate, n is the amount of times the interest is compounded per time period, and t is the amount of time.
In our case, we need to find the time t. Then, by moving the Principal to the left hand side, we get
[tex]\frac{A}{P}=(1+\frac{r}{n})^{nt}[/tex]By applying natural logarithm on both sides, we get
[tex]\ln (\frac{A}{P})=nt\cdot ln(1+\frac{r}{n})[/tex]now, we can isolate t as
[tex]t=\frac{\ln (\frac{A}{P})}{n\ln (1+\frac{r}{n})}[/tex]Now, we can substitute our given values into this expression. It yields,
[tex]t=\frac{\ln (\frac{6550}{6000})}{12\ln (1+\frac{0.1}{12})}[/tex]which gives
[tex]t=\frac{0.0877}{12(0.0083)}[/tex]then, the time (in years) is
[tex]t=0.88\text{ years}[/tex]Now, we must convert this result in months. Since 1 year has 12 months, we have
[tex]\begin{gathered} t=0.88\times12 \\ t=10.56\text{ months} \end{gathered}[/tex]that is, the answer is 10.56 months
Factor xy+qr-xr-qy using grouping method
We are given the following expression:
[tex]xy+qr-xr-qy[/tex]We will associate the terms that have common factors, like this:
[tex](xy-xr)+(qr-qy)[/tex]Now we take the common factor for each of the parenthesis:
[tex]x(y-r)+q(r-y)[/tex]Since each parenthesis has a common factor but with inverted signs, we will take -1 as a common factor in the second parenthesis, we get:
[tex]x(y-r)-q(y-r)[/tex]Now we can take "y-r" as a common factor for the entire expression:
[tex](y-r)(x-q)[/tex]And thus we have factored the expression.
4. What is the value of c in the quadratic equation 2m² + m +3 = 0?A.OB. 1C. 2D. 3
GIven a quadratic equation in standard form, we have
[tex]\begin{gathered} ax^2+bx+c=0 \\ \text{where} \\ a,b,\text{ and }c\text{ are the coefficients of the terms} \end{gathered}[/tex]c represents the coefficient of the constant in the quadratic equation.
Given the equation 2m² + m +3 = 0
felicia borrowed $12,000 from her bank at a monthly interest rate of 5%. if she paid back the loan after 3 months, how much interest is she going to pay? how much money will she pay back to her bank?
felicia borrowed $12,000 from her bank at a monthly interest rate of 5%. if she paid back the loan after 3 months, how much interest is she going to pay? how much money will she pay back to her bank?
we have that
the interest for each month is
0.05*12,000=$600
after 3 months
total interest is 3*$600=$1,800
she going to pay $1,800
Part b
12,000-1,800=$10,200
Today, full-time college students report spending a mean of 27 hours per week on academic activities, both inside and outside the classroom. Assume the standard deviation of time spent on academic activities is 4 hours. If you select a random sample of 16 full-time college students, a. what is the probability that the mean time spent on academic activities is at least 26 hours per week? b. there is an 85% chance that the sample mean is less than how many hours per week? c. If you select a random sample of 64 full-time college students, there is an 85% chance that the sample mean is less than how many hours per week?
(a) The probability that the mean time spent on academic activities is at least 26 hours per week is 0.317.
(b) If 64 random full-time college students are selected, there is an 85% chance that the sample mean is less than 27.52 hours.
Full-time college students report spending a mean of 27 hours per week on academic activities, both inside and outside the classroom. Assume the standard deviation of time spent on academic activities is 4 hours.
In a set with mean μ, the standard deviation σ and the z score of measure X is given by:
Z = ( X - μ )/σ
The theorem of central limits: According to this, the sample mean with size n can be roughly compared to a normal distribution with mean and standard deviation for a normally distributed random variable, X, with mean and standard deviation:
s = σ/√n
(a) In this we have to find the probability that the mean time spent on academic activities is at least 26 hours per week,
s = σ/√n
s = 4/√16
s = 4/4 = 1
Therefore, 1 is subtracted from the p-value of Z when X = 28.
So,
Z = ( X - μ )/σ
Z = ( 28 - 27)/1 = 1
For Z = 1 the p-value is 0.317.
(b) If 64 full-time college students are selected randomly.
85% chance that the sample mean is less.
s = σ/√n = 4/√(64) = 4/8 = 1/2 = 0.5
When the p-value is 0.85, Z = 1.04
Z = ( X - μ )/σ
1.04 = ( X - 27)/0.5
X - 27 = 0.52
X = 27.52
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Your younger brother just heard about the 50-20-30 savings rule of thumb and asks you what it is. What do you tell him?
The 50-20-30 savings rule is a simple plan that helps people on managing their money.
It states that over your total after-tax earnings, 50% should be spent on your needs and obligations. 20% should be spent on savings and debt payments, and 30% on whatever else you like.
7 x+2 1 3. Add/Subtract: + Simplify and state the domain. 2x + 2 4 x+1 4. Subtract: 4 x2-3x+2 Simplify and state the domain. 3x - 3 Ź 5. Add Subtract: 2 3x-5 x2-7x 2x – 14 Simplify and state the domain.
Answer:
Explanation:
Given the below;
[tex]\frac{1}{2}+\frac{15}{2x-14}-\frac{3x-5}{x^2-7x}[/tex]To simplify the above, we have to 1st find the LCM of 2, 2x - 14, and x^2 - 7x which is 2x(x - 7), so we'll have;
[tex]\frac{x(x-7)+15x-2(3x-5)}{2x(x-7)}[/tex]Let's go ahead and simplify;
[tex]undefined[/tex]I need help this is geometry 
Answer: 6 a: 1=30 2=44, 3=106 4=30
Step-by-step explanation:
well, 3 is the opposite of 106 so they are equal, 2 is the opposite of 44 so they are equal, then you can just take the straight line and subtract the ones around it from 180 to find the 1 or 4, so 180-106, then 74-44=30. then because 1 and 4 are on opposite sides, they are equal. Sorry for not having enough times for all problems, but to help with 6 and 7, just remember that opposites are equal (you can use in 6b and 7a) and the if they make a straight line they make 180 degrees (use in 7b)
Can you please help draw this loci?The locus of point in the interior of the square ABCD AND ALSO equidistant from its side AB and BC is diagonal BD.
First let's draw the square ABCD:
The point is interior to the square, and also is equidistant from the sides AB and BC.
Drawing all the points that follow these rules in green, we have:
So this loci is represented by the diagonal BD of the square. All the points of this diagonal are equidistant to the sides AB and BC.
At a movie premiere the movie co-workers were asked whether they liked it or did not like it .of the 20 adult asked 15 of them said they liked it a 50 teenagers asked 32% said they liked it .Fill in the blank below to make a statement the most reasonable possible.At the movie premiere ____ moviegoers enjoyed the Movie more because only ___% did not like the movie where is ___% of the ___ moviegoers did not like the movie.
Answer:
At the movie premiere, adult moviegoers enjoyed the movie more because only 25% did not like the movie whereas 68% of the teenager moviegoers did not like the movie.
First, let us get the percentage of adults that liked the movie.
It is said that 15 out of 20 adults liked the movie. We can get the percentage by dividing the number of adults who liked the movie by the total number of adults.
[tex]\frac{\text{ number of adults who liked the movie }}{\text{ total number of adults }}=\frac{15}{20}\times100=75\%[/tex]We will then find out the percentage of adults and teenagers that did not like the movie by subtracting the percentage that liked the movie from 100%
Adults who did not like the movie:
[tex]100\%-75\%=25\%[/tex]Teenagers who did not like the movie:
[tex]100\%-32\%=68\%[/tex]Here, we can conclude that:
At the movie premiere, adult moviegoers enjoyed the movie more because only 25% did not like the movie whereas 68% of the teenager moviegoers did not like the movie.
Gregory had $7.32 he put $3.50 in the bank how much did he have left to spend
Answers
$3.82
Explanation
If Gregory had $7.32 he put $3.50 in the bank, the the amount left to spend is ($7.32 - $3.50) = $3.82
Write a function $g$ whose graph represents the indicated transformation of the graph of f the equation f(x)=x+2 translated 2 units to the right is g(x)=
The function g(x) whose graph represents the indicated transformation of the graph of the equation f(x) = x+2 translated 2 units to the right is g(x) = x
Here the function is
f(x) = x+2
It is translated 2 units to the right
A translation defined as the movement of the graph either horizontally or vertically. In translation the shape or the size of the graph will not change only the location of the graph changes
Then the equation will be
f(x-2) = (x-2)+2
= x-2+2
= x
Hence, the function g(x) whose graph represents the indicated transformation of the graph of the equation f(x) = x+2 translated 2 units to the right is g(x) = x
The complete question is
Write a function g(x) whose graph represents the indicated transformation of the graph of f the equation f(x)=x+2 translated 2 units to the right.
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8X squared +4x-112=0
8x² + 4x - 112 = 0
To solve this equation, we can use the quadratic formula, as follows:
[tex]\begin{gathered} x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x_{1,2}=\frac{-4\pm\sqrt[]{4^2-4\cdot8\cdot(-112)}}{2\cdot8} \\ x_{1,2}=\frac{-4\pm\sqrt[]{16+3584^{}}}{16} \\ x_{1,2}=\frac{-4\pm\sqrt[]{3600^{}}}{16} \\ x_1=\frac{-4+60}{16}=3.5 \\ x_2=\frac{-4-60}{16}=-4 \end{gathered}[/tex]a right triangle has an angle measure of 18.4 what is the value of x the missing angle
The value of x is 71.6 degrees
How to find third angle :The sum of a triangle's interior angles equals 180o. When the other two angles of a triangle are known, subtract the number of degrees in the other two angles from 180 degrees to find the third angle. A triangle has three parallel straight sides. The lengths of the sides can vary, but the largest side's length cannot be equal to or greater than the sum of the other two sides. Furthermore, a triangle has three interior angles, the sum of which is always 180 degrees.
We have a Right angle triangle and a value of an angle 18.4.
That is one angle is 18.4° and other is 90°.
To find third angle just add two angles and subtract that with 180.
Add two angle we have 18.4 + 90 = 108.4Subtract 108.4 with 180 = 180 -108.4 = 71.6°The third angle is 71.6°
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What is the length of the missing leg? If anyone to help it would be much appreciated
In the given right triangle
Applying the Pythagorean Theorem
[tex]73^2=b^2+55^2[/tex]Solve for b
[tex]\begin{gathered} b^2=73^2-55^2 \\ b^2=2,304 \\ b=48\text{ in} \end{gathered}[/tex]
Which of the following expressions are perfect-square trinomials? Check all of the boxes that apply.
x²-16x-64
4x2 +12x+9
x+20x+100
x² + 4x + 16
Answer:
The second and the third one
Step-by-step explanation:
4x^2 + 12x + 9 = (2x + 3)^2
x^2 + 20x + 100 = (x + 10)^2
A car rental agency charges $175 per week plus $0.20 per mile to rent a car. How many miles can you travel in one week for $295?
Answer:
600 miles
Step-by-step explanation:
295$ - 175$ = 120$. 120$ divided by 20 cents equals 600.
Distribute the following: 1.9 (3 + 2) 2.11 ( 4 - 1) 3.12 ( 7 + 7) 4.5 (4 + 8) 5.10 (9 - 5)
1.
9 (3+2)
We have to distribute number 9 in the parenthesis, multiply each term in the parenthesis by 9:
9(3)+9(2)
27+18
45
2.
11(4-1)
11(4)+11(-1)=44-11=33
3.
12(7+7)
12(7)+12(7)
84+84
168
4.
5 (4+8)
5(4)+5(8)
20+40
60
5.
10(9-5)
90-50
40
May I please get help describing each? I have tried multiple times to get each of them are
Definitions:
Perpendicular bisector: A line that bisects (split into two equal parts) a line segment at a right angle (90°)
Angle bisector: A line that bisects a angle.
Median of a triangle: Line segment drawn from a vertex to the middpoint of the opposite side to the vertex.
Altitude of a triangle: Perpendicular segment form a vertex of a triangle to the opposite side.
a) With the given information you can describe FI as:
Median of triangle FGH:Line segment drawn from a vertex (F) to the middpoint of the opposite side to the vertex (GH). The two marks in red indicates that the segments have the same measure (then the point I is the middpoint of the side GH.
Theres is not indication of a perpendicular angle, or a bisection of the angle. Then you can not describe FI as any of the other options.
Determine the center and radius of the following circle equation:x2+y2−14x−10y−26=0x 2 +y 2 −14x−10y−26=0
To determine the center of the circle;
x² + y² - 14x - 10 y - 26 = 0
we have to make the above equation to be in the form;
(x-a)² + (x-b)² = r²
where (a,b) is the center of the circle and r is the radius of the circle
x² + y² - 14x - 10 y - 26 = 0
add 26 to both-side of the equation
x² + y² - 14x - 10 y - 26 + 26 = 0 + 26
x² + y² - 14x - 10 y = 26
x² - 14x +y² - 10y = 26
add square of half of each coefficient
x² - 14x + (-7)² + y² -10y + (-5)² = 26 + (-7)² + (-5)²
(x -7)² + (y-5)² =
(
Match the vocabulary to the proper definition?1.)two-way frequency table2.)categorical variable3.)marginal frequencies4.)joint frequencies-----------------Definitions:----------------()entries in the TOTAL row and TOTAL column of a two-way frequency table()entries in the body of a two-way frequency table () variables that take on values that are names or labels. The color of a ball, gender, or year in school (freshman, sophomore, junior, senior) are examples of categorical variables ()a useful tool for examining relationships between categorical variables
1. Two-way frequency table
entries in the body of a two-way frequency table
2. Categorical variable
variables that take on values that are names or labels. The color of a ball, gender, or year in school (freshman, sophomore, junior, senior) are examples of categorical variables
3. Marginal frequencies
entries in the TOTAL row and TOTAL column of a two-way frequency table
4. Joint frequencies
a useful tool for examining relationships between categorical variables
3r^2+27[tex]3r { +}^{2} + 27 = 0[/tex]
Solution
For this case we have the following:
[tex]3r^2+27=0[/tex]We can subtract 27 in both sides and we got:
[tex]3r^2=-27[/tex]Then we can divide both sides by 3 and we got:
[tex]r^2=-9[/tex]Then the possible to solution are:
[tex]r=3i,r=-3i[/tex]The length between the bases on a baseball field is 90ft. A scale drawing shows the distance between the based as 2 1/2 inches. One inch on this drawing equals how many ft?
SOLUTION:
Step 1:
In this question, we have the following:
The length between the bases on a baseball field is 90ft.
A scale drawing shows the distance between the bases is 2 1/2 inches.
One inch on this drawing equals how many ft?
Step 2:
[tex]\begin{gathered} \text{90 f}eet\text{ =2 }\frac{1}{2}\text{ inches} \\ y\text{ f}eet\text{ = 1 inch} \end{gathered}[/tex]Cross-multiply, we have that:
[tex]\begin{gathered} 2\frac{1}{2}\text{ x y = 9}0\text{ x 1} \\ \frac{5}{2}y=90 \\ \text{Divide both sides by }\frac{5}{2},\text{ we have that:} \\ y\text{ = 90 x }\frac{2}{5} \\ y\text{ =}\frac{180}{5} \\ y\text{ =36} \end{gathered}[/tex]CONCLUSION:
One inch on this drawing equals 36 feet
Round 1436.1406616345 to one decimal place as needed
We want to round up to one decimal place;
The number after the decimal should be rounded up to the nea
[tex]1436.1406616345\approx1436.1[/tex]3 Find the co-ordinates of the point at which the gradient of the curve with equation y = 3x² has gradient 18.
The co-ordinates of the point at which the gradient of the curve y = 3x² is 18 are (3, 27).
Here we are given the equation of a curve as- y = 3x²
The gradient of a curve can be found out by differentiating it with respect to the independent variable. Thus, the gradient here will be dy/dx.
dy/dx = 6x
Thus the gradient of the curve is 6x.
Further, we are given that the gradient value is 18. thus, the value of x at gradient = 18 will be-
6x = 18
x = 18/6
x = 3
Substituting this in the equation of the curve, we can find the value of y as follows-
y = 3*3²
y = 3*9
y = 27
Thus, the co-ordinates of the point at which the gradient of the curve y = 3x² is 18 are (3, 27).
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2015 > Chapter 1: Chapter 1 Review Exercises > Section Exercises 1 > Exercise 23
23
The formula F =
(K-273.15) +32 converts a temperature from kelvin K to degrees Fahrenheit F.
a. Solve the formula for K.
K=
b. Convert 180°F to kelvin K. Round your answer to the nearest hundredth.
The solution is about K.
The most appropriate choice for subject of a formula will be given by -
180° F has been converted to 355.35 K
What is subject of a formula?
Subject of a formula is the variable which is expressed in terms of other variables present in the formula.
Here,
[tex]F = \frac{9}{5}(K - 273.15) + 32\\F - 32 = \frac{9}{5}(K - 273.15)\\K = \frac{5}{9}(F - 32)+273.15[/tex]
Putting F = 180
[tex]k = \frac{5}{9}(180 - 32) + 273.15\\K=\frac{5}{9}\times 148+273.15\\K=82.2 + 273.15\\K=355.35[/tex]
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A group of 4 students went to the movie theater. They each bought a ticket for $x and spent $10.50 each on snacks. A group of 3 adults went to the movie theater and paid twice as much for each of their tickets as each student. The group of adults also spent $10.00 each on snacks. The group of students spent the same amount as the group of adults. What is the cost of each adult ticket? The cost of each adult ticket is $__
Explanation
Step 1
Let x represents the cost for the students ticket
Let y represents the cost for the adult ticket
1)A group of 4 students went to the movie theater. They each bought a ticket for $x and spent $10.50 each on snacks
then
[tex]\begin{gathered} \text{total}=4x+4(10.50) \\ total=4x+42 \end{gathered}[/tex]2)A group of 3 adults went to the movie theater and paid twice as much for each of their tickets as each student. The group of adults also spent $10.00 each on snacks
