Caroline's gross annual salary is $47,448 What is the max amount of rent she can afford to pay?

Will give BRAINLIEST. Thank you! Double checking.

Answer:

155 lbs.

Step-by-step explanation:

69.75 g of protein divided by 0.45= 155

Answer: He weighs 155 lbs.

Step-by-step explanation:

Since we have given that

Amount of protein he used = 69.75 g

Factor = 0.45

We need to find the weight of an individual.

So, Weight of an individual is given by

[tex]Weight\times factor=Protein\\\\Weight=\dfrac{Protein}{Factor}[/tex]

[tex]=\dfrac{69.75}{0.45}\\\\=155\ lbs[/tex]

Hence, he weighs 155 lbs.

[tex] - {x}^{2} - 4x + 15 \\ = - {x}^{2} - 4x - 4 + 15 + 4 \\ = - ( {x}^{2} + 4x + 4) + 19 \\ = \underbrace{- {(x + 2)}^{2}}_{ \leqslant 0} + 19 \\ \Rightarrow - {(x + 2)}^{2} + 19 \leqslant 19 \\ \Rightarrow Maximum \: value \: is \: 19 \: as \: x=-2

[/tex]

Answer:

Option b

Step-by-step explanation:

The equation [tex]4x ^ 2 + 5y ^ 2 = 20[/tex] has center in (0,0).

But the transformation [tex]T(5, -6)[/tex] shifts the center of the equation to the point (5, -6).

Therefore, when applying [tex]T(5, -6)[/tex] we will have the following equation translated.

[tex]4(x-5) ^ 2 + 5(y - (-6)) ^ 2 = 20[/tex].

Simplifying we have:

[tex]4(x-5) ^ 2 + 5(y + 6) ^ 2 = 20[/tex]

Now we expand [tex](x-5) ^ 2[/tex] and [tex](y + 6) ^ 2[/tex]

[tex]4(x ^ 2 -10x +25) + 5(y ^ 2 + 12y +36) = 20\\\\4x ^ 2 -40x + 100 + 5y ^ 2 + 60y + 180 = 20\\\\4x ^ 2 + 5y ^ 2 -40x + 60y +260 = 0[/tex]

The equation of a circle has the form

[tex]h(x-a) ^ 2 + q(y-b) ^ 2 = r[/tex]

For h = 1 and q = 1.

If [tex]h \neq 1[/tex] and [tex]q\neq 1[/tex] then the graph becomes an ellipse.

In this problem h = 4 and q = 5 therefore the figure is an ellipse

Answer:

48 miles

Step-by-step explanation:

The volume of a sphere with a radius of 4 centimeters is calculated using the formula V = (4/3)πr³. Substituting 4 cm for the radius and 3.14 for π, the volume is approximately 268 cubic centimeters.

To calculate the volume of a sphere with a given radius, you can use the formula V = (4/3)πr³, where V represents the volume and r is the radius. In our case, the radius is 4 centimeters. Substituting the values into the formula gives us V = (4/3) * 3.14 * (4 cm)³.

Performing the calculation: V = (4/3) * 3.14 * 64 cm³ = 267.94666666666666 cm³. Therefore, the volume of the sphere is approximately 268 cm³ when rounded to a whole number.

Answer: [tex]b=10^3[/tex]

Step-by-step explanation:

You know that there are 10 blueberries in each muffin. There are 10 muffins in each box and the total number of boxes is 10.

Then, to calculate the total number of blueberries, you need to multiply the total number of boxes by the number of muffins in each box and multiply this by the number of blueberries in each muffin.

Let be "b" the total number of blueberries. Then:

[tex]b=10*10*10[/tex]

By the Product of powers property:

[tex]a^m*a^n=a^{(m+n)}[/tex]

Then you can write the expression:

[tex]b=10^3[/tex]

To find the sale price of a $384 skateboard with a 24% discount, convert the paid percentage to a decimal (76% to 0.76) and multiply with the original price, resulting in a sale price of $291.84.

To calculate the sale price of a skateboard originally priced at $384 with a 24% discount, we first need to determine what percentage of the original price will actually be paid. Since the discount is 24%, that means 76% of the original price will be paid (100% - 24% = 76%). To convert this percentage to a decimal, we divide by 100, getting 0.76.

Next, we find the sale price by multiplying the original price by the decimal form of the percentage paid:
$384 × 0.76 = $291.84 as the sale price of the skateboard.

Answer:

2nd graph

Step-by-step explanation:

Exponential increase will be a graph that increase all throughout and the rate of increase "increases" with age.

The 2nd graph is correct because it shown "increase" as well as "exponential" increase (the rate of increase increases).

Answer: 2nd graph

Your answer is going to be the second graph

They need about 9 vans.

To find the equation of the perpendicular bisector, find the midpoint of the line segment and determine the slope of the perpendicular line.

To find the equation of the perpendicular bisector of a given line segment, we need to find the midpoint of the segment and then determine the slope of the perpendicular line. Let's denote the coordinates of the endpoints of the line segment as (x1, y1) and (x2, y2). The midpoint of the segment can be found using the formula:

M = ((x1 + x2) / 2, (y1 + y2) / 2)

The slope of the perpendicular line can be found using the negative reciprocal of the slope of the given line segment:

Perpendicular slope = -1 / slope of given line segment

Once we have the midpoint and the slope of the perpendicular line, we can use the point-slope form of a linear equation to write the equation of the perpendicular bisector:

y - y1 = perpendicular slope * (x - x1)

Multiply total sales by 11%

4265 x 0.11 = 469.15

His commission was $469.15

Final answer:

Wilson Green's commission is calculated by multiplying his total sales of $4265.00 by his commission rate of 11 percent, which equals $469.15.

Explanation:

Wilson Green earns an 11 percent commission on every home security system he sells. For the month, his total sales amounted to $4265.00. To calculate Wilson's commission, we need to find 11 percent of $4265.00.

The formula for calculating the commission is:

Commission = Total Sales × Commission Rate

By plugging in the numbers:

Commission = $4265.00 × 0.11

Now, let's do the math:

Commission = $469.15

Therefore, Wilson's commission for the month is $469.15

Answer:

Step-by-step explanation:

[tex]x^2-2x+17=0\qquad\text{subtract 17 from both sides}\\\\x^2-2x=-17\\\\x^2-2(x)(1)=-17\qquad\text{add}\ 1^2\ \text{to both sides}\\\\x^2-2(x)(1)+1^2=-17+1^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(x-1)^2=-17+1\\\\(x-1)^2=-16<0\Rightarrow\boxed{\text{NO REAL SOLUTION}}\ because\ x^2\geq0\\\\\text{In the set of complex numbers}\\\\i=\sqrt{-1}\\\\(x-1)^2=-16\iff x-1=\pm\sqrt{-16}\\\\x-1=-\sqrt{(16)(-1)}\ \vee\ x-1=\sqrt{(16)(-1)}\\\\x-1=-\sqrt{16}\cdot\sqrt{-1}\ \vee\ x-1=\sqrt{16}\cdot\sqrt{-1)[/tex]

[tex]x-1=-4i\ \vee\ x-1=4i\qquad\text{add 1 to both sides}\\\\x=1-4i\ \vee\ x=1+4i[/tex]

Answer:

B

Step-by-step explanation:

The exponential function is the function of the form

[tex]y=a\cdot b^x,[/tex]

where [tex]b[/tex] is the base and [tex]a[/tex] is the initial value.

The function [tex]y=x^2[/tex] is the quadratic function, which cannot be represented as [tex]y=a\cdot b^x.[/tex] Thus, this function is not exponential.

Answer:

The answer is B.

Step-by-step explanation:

Answer:

The answer is hyperbola; (x')² - (y')² - 16 = 0 ⇒ answer (a)

Step-by-step explanation:

* At first lets talk about the general form of the conic equation

- Ax² + Bxy + Cy²  + Dx + Ey + F = 0

∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.

∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.

∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.

* Now we will study our equation:

 xy = -8

∵ A = 0 , B = 1 , C = 0

∴ B² - 4 AC = (1)² - 4(0)(0) = 1 > 0

∴ B² - 4AC > 0

∴ The graph is hyperbola

* The equation xy = -8

∵ We have term xy that means we rotated the graph about

  the origin by angle Ф

∵ Ф = π/4

∴ We rotated the x-axis and the y-axis by angle π/4

* That means the point (x' , y') it was point (x , y)

- Where x' = xcosФ - ysinФ and y' = xsinФ + ycosФ

∴ x' = xcos(π/4) - ysin(π/4) , y' = xsin(π/4) + ycos(π/4)

∴ x' = x/√2 - y/√2 = (x - y)/√2

∴ y' = x/√2 + y/√2 = (x + y)/√2

* Lets substitute x' and y' in the 1st answer

∵ (x')² - (y')² - 16 = 0

∴ [tex](\frac{x-y}{\sqrt{2}})^{2}-(\frac{x+y}{\sqrt{2}})^{2}=[/tex]

 ( [tex]\frac{x^{2}-2xy+y^{2}}{2})-(\frac{x^{2}+2xy+y^{2}}{2})-16=0[/tex]

* Lets open the bracket

∴ [tex]\frac{x^{2}-2xy+y^{2}-x^{2}-2xy-y^{2}}{2}-16=0[/tex]

* Lets add the like terms

∴ [tex]\frac{-4xy}{2}-16=0[/tex]

* Simplify the fraction

∴ -2xy - 16 = 0

* Divide the equation by -2

∴ xy + 8 = 0

∴ xy = -8 ⇒ our equation

∴ Answer (a) is our answer

∴ The answer is hyperbola; (x')² - (y')² - 16 = 0

* Look at the graph:

- The black is the equation (x')² - (y')² - 16 = 0

- The purple is the equation xy = -8

- The red line is x'

- The blue line is y'

Answer:

a. hyperbola;

Answer:

Step-by-step explanation:

If y = 2x + 1, then dy/dt = 2(dx/dt).

If y = 2x + 1, then y = 2(40) + 1 when 40 is substituted for x.  y = 81.

(a) if dx/dt = 3, find dy/dt when x = 4:

       Replacing dx/dt with 3 in dy/dt = 2(dx/dt) yields dy/dt = 2(3) = 6.

(b) if dy/dt = 2, find dx/dt when x = 40:

        Replacing dy/dt with 2 in dy/dt = 2(dx/dt) results in 2 = 2(dx/dt), so dx/dt must be 1.

First, you differentiate the given function. Next, apply the chain rule which states dy/dt = dy/dx * dx/dt. Substitute the known values to find dy/dt. For the second part, rearrange the chain rule to find dx/dt = dy/dt / dy/dx and substitute the known values.

This question deals with the basic application of the chain rule in differentiation. The given function is y = 2x + 1, where both y and x are functions of t. You are supposed to determine dy/dt and dx/dt.

(a) First, differentiate y = 2x + 1 with respect to x to obtain dy/dx = 2. According to the chain rule in calculus, dy/dt = dy/dx * dx/dt. Substituting the known values from the question, we have dy/dt = 2 * 3 = 6 when x = 4.

(b) For dy/dt = 2, you need to rearrange dy/dt = dy/dx * dx/dt to find dx/dt = dy/dt / dy/dx. As dy/dx = 2, you can evaluate dx/dt = 2 / 2 = 1 when x = 40.

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Answer:

Step-by-step explanation:

[tex]\text{The quadratic equation:}\ ax^2+bx+c=0.\\\\\text{We have}\ x^2-4x+2=0\\\\a=1,\ b=-4,\ c=2\\\\\text{Substitute to}\ b^2-4ac:\\\\b^2-4ac=(-4)^2-4(1)(2)=16-8=8[/tex]

Answer:

72 voters

Step-by-step explanation:

Total surveyed members: 40

Total members with a yes vote: 12

Percentage of the voters (voting yes): [tex]\frac{12}{40} * 100 = 30%[/tex]

From analysis, it is observed that 30% of the voters are expected to vote yes in a sample.

Therefore, the number of voters expected to vote yes out of 240 are: 30% of 240

=> [tex]\frac{30}{100} * 240 = 72[/tex]

Answer:

72 voters

Step-by-step explanation:

[tex]\displaystyle\\6<\sqrt[3]{x}<7~~~\Big|^3\\\\6^3<\Big(\sqrt[3]{x}\Big)^3<7^3\\\\216<x<343\\\\\boxed{x\in\{217,~218,~219,~220,~\cdots~,~340,~341,~342\}}[/tex]

.

Answer:

Step-by-step explanation:

The value would be 6.5

Solving the system of equation, we get Option (C) (2,-1).

The equations given are 2x - y = 5 and 3x + 2y = 4.

To find the point which solves the two equation, we have to satisfy the given x and y coordinates of the point on the given two equations.

Checking all the other Options, it does not satisfies except Option (C).

Checking the point (2,-1) on the first equation 2x - y = 5 , we get 5 in the left hand side of the equation.

Again checking the point (2,-1) on the second equation 3x + 2y = 4 , we get 4 in the left hand side of the equation.

Therefore the coordinates (2,-1) (Option C) satisfies both the equation which is the required solution.

To learn more about solving system of equation, refer -

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Answer:13

Step-by-step explanation:you have to divide it  

The area of a sector is found using the formula :

Area = πr^2(angle/360)

R is given as 6 meters and the angle is given as 78 degrees.

Area = π * 6^2 * (78/360)

Area = π * 36 * 0.21666

Area = π * 7.8

Area = 7.8π square meters. ( Exact area in terms of PI)

or using 3.14 for PI: Area = 24.492 square meters.

Round the decimal area as needed.

Answer:

The shape of the mat is a square

Step-by-step explanation:

we know that

The area of the rectangle (An Olympic floor exercise mat) is equal to

[tex]A=LW[/tex]

we have that

[tex]A=144\ ft^{2}[/tex]

[tex]L=12\ ft[/tex]

substitute the values and solve for W

[tex]144=12W[/tex]

[tex]W=144/12=12\ ft[/tex]

so

The length is equal to the width

therefore

The shape of the mat is a square

Answer:

2+2 is 4

Step-by-step explanation:

Answer:

im doing just find what about you mate

Step-by-step explanation:the answer  is 4

Answer:

The correct answer option is 0.67.

Step-by-step explanation:

We are given that the probability that a child eats popcorn and cotton candy is 0.58, probability that a child eats popcorn is 0.69 and the probability that a child eats cotton candy is 0.87.

We are to find the probability that a child eats popcorn given that the child has already eaten cotton candy.

P (eats popcorn and has already eaten cotton candy) = [tex]\frac{0.58}{0.87}[/tex] = 0.67

The mode is the number that appears most often.

Looking at the chart, there are two 1's on the right side, so the mode would be 31

To construct a 90% confidence interval for the average number of customers who visit the salon on weekdays, calculate the sample mean and standard deviation, determine the critical t-value, and use the confidence interval formula to find the range.

To construct a 90% confidence interval for the average number of customers who visit the salon on weekdays, we first calculate the sample mean and the sample standard deviation. The sample mean is the average of the seven data points (40, 30, 28, 22, 36, 16, and 50), which is 32. The sample standard deviation is the measure of variability in the data, which is calculated to be approximately 12.11.

Next, we determine the critical t-value for a 90% confidence interval with 6 degrees of freedom (7 data points minus 1). We can find this value in the t-distribution table or use statistical software, and it is approximately 1.943.

Finally, we can calculate the confidence interval using the formula: Confidence interval = sample mean ± (t-value * standard deviation / square root of sample size). Plugging in the values, we get the confidence interval as (23.52, 40.48). Therefore, we can be 90% confident that the average number of customers who visit the salon on weekdays falls within this range.

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The correct equation representing the time Bailey spends in the weight room each week is 2w=3. By solving this equation, we find Bailey spends 1.5 hours in the weight room each week.

The question tells us that Baily spends 3 hours each week playing soccer and this is two times the amount of time she spends working out in the weight room. We can represent the time she spends in the weight room as w. So, the question gives us the equation 2w=3. Since 2 times what number gives us 3, we can solve for w by dividing both sides of the equation by 2. When we do this, we have w=3/2, which means Baily spends 1.5 hours in the weight room each week.

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Looks like the limit is

[tex]\displaystyle\lim_{x\to\pi/2^+}\frac{\cos x}{1-\sin x}[/tex]

which yields an indeterminate form [tex]\dfrac00[/tex]. Rewriting as

[tex]\dfrac{\cos x(1+\sinx)}{(1-\sin x)(1+\sin x)}=\dfrac{\cos x(1+\sin x)}{1-\sin^2x}=\dfrac{1+\sin x}{\cos x}[/tex]

we see the numerator approaches 1 + 1 = 2, while the denominator approaches 0. Since [tex]\cos x<0[/tex] for [tex]x[/tex] near [tex]\dfrac\pi2[/tex] with [tex]x>\dfrac\pi2[/tex], the limit is [tex]-\infty[/tex].

Answer:

28.26

Step-by-step explanation:

The circumference of a circle is the distance around the edge of the circle. To find the circumference, we use the formula C = 2πr. The area of the circle is the amount inside the circle and is found using A = πr². Substitute the relevant values in each situation into the formulas to find the circumference and/or area.

Substitute C = 18.84 and solve for r. Then substitute r into the area formula.

C = 2πr

18.84 = 2πr

3 = r

A = πr² = π(3)² = 28.26

Answer:

28.26

Step-by-step explanation: