Which shows the graph of the solution set of 6x + 4y < 12? On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (3, 1). Everything below and to the left of the line is shaded. On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (3, 1). Everything above and to the right of the line is shaded. On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (2, 0). Everything to the left of the line is shaded. On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (2, 0). Everything to the right of the line is shaded.

Answer:

The monthly cost function for the scenario C(x,y) is;

C(x,y) = 70,000 + 2900x + 800y

Step-by-step explanation:

Let C represent the monthly cost in dollars.

x represent the number of performances by the cabaret artist per month

and y represent the number of hours of jazz per month

Given;

monthly costs of $70,000

regular cabaret artist is charging you $2900 per performance.

Per month = $2900x

your jazz ensemble is charging $800 per hour.

Per month = $800y

The monthly cost function for the scenario C(x,y) is the sum of all the costs;

C(x,y) = 70,000 + 2900x + 800y

Answer:

If the side length of a square is 4 inches, it's Area is 16 inches, and Perimeter is 16 inches.

Step-by-step explanation:

Given that the Area = s²

Perimeter = 4s

Side length of the square = s

If the length of a square is 4 inches, then applying the above formulas, we have

s = 4 inches

Area = 4² = 16 inches

Perimeter = 4s = 4×4 = 16 inches

Final answer:

The area of a square with a side length of 4 inches is 16 square inches and its perimeter is 16 inches. Doubling the side length to 8 inches yields an area that is four times greater, 64 square inches, due to the squared relationship between side length and area.

Explanation:

Understanding Square Area and Perimeter

A student has posed a question about the properties of squares. We are given that the side length of a square is 4 inches. From this, we can calculate the square's area and perimeter. The area of a square is found by squaring the length of its side (s2), which in this case would be 4 inches × 4 inches = 16 square inches. The perimeter is the length around the square, calculated by multiplying the side's length by 4, yielding 4 inches × 4 = 16 inches.

By understanding the formulas for area (s2) and perimeter (4s), students can solve many geometrical problems related to squares. For instance, if the dimensions of a square are to be doubled, the new side length would be 4 inches × 2 = 8 inches, resulting in an area of 8 inches × 8 inches = 64 square inches, which is four times the original area, demonstrating that the area scales with the square of the linear dimensions.

Answer:

298 pictures

Step-by-step explanation:

One coloring book has 134 pictures, and other one has 309 pictures. The total will be addition:

134 + 309 = 443 pictures

Rachel colored 145 of them all, so subtract 145 from 443:

443 - 145 = 298

She still has 298 pictures left.

Answer:

298

Step-by-step explanation:

Total pictures:

134 + 309

443

Already coloured: 145

To be coloured: 443 - 145

= 298

Step-by-step explanation:

10x2 + 50x

10x ( x +5)

Is the result

Answer:

If we want to guarantee a decrease in the width of the confidence interval we need to analyze the margin of error given by:

[tex] ME = t_{\alpha/2} \frac{s}{\sqrt{n}}[/tex]

The width of the confidence interval is just defined as two times the margin of error:

[tex] Width = 2ME[/tex]

And then we can decrease this width of the interval we need to increase the sample size in order to have a greater number in the denominator for the margin of error and that implies a reduction in this width for the confidence interval at the confidence level fixed of 99%

By the other hand if we increase the confidence level then the width would be larger and in the other case when we decrease the confidence level the width would be lower.

Step-by-step explanation:

For this case w ehave the following info given from the problem

[tex] n =17[/tex] represent the sample size for the cars selected

[tex]\bar X = 12260[/tex] represent the average price for the cars sold

[tex] s= 800[/tex] represent the standard deviation for the solds

And we have a 99% confidence interval for the true average price for the cars given:

[tex]11693 \leq \mu \leq 12827[/tex]

And we know that the confidence interval for the true mean is given by this formula:

[tex] \bar X \pm t_{\alpha/2} \frac{s}{\sqrt{n}}[/tex]

If we want to guarantee a decrease in the width of the confidence interval we need to analyze the margin of error given by:

[tex] ME = t_{\alpha/2} \frac{s}{\sqrt{n}}[/tex]

The width of the confidence interval is just defined as two times the margin of error:

[tex] Width = 2ME[/tex]

And then we can decrease this width of the interval we need to increase the sample size in order to have a greater number in the denominator for the margin of error and that implies a reduction in this width for the confidence interval at the confidence level fixed of 99%.

By the other hand if we increase the confidence level then the width would be larger and in the other case when we decrease the confidence level the width would be lower.

Answer:

Question1:volume=6600cm^3

Question2:cost=$441.18

Step-by-step explanation:

Question 1:

volume=length x width x height

Volume=15 x 20 x 22

Volume=6600cm^3

Question 2:

area of kitchen=length x width

Area of kitchen=18 x 19

Area of kitchen=342ft^2

$1.29 for 1ft^2

$b for 342ft^2

$b=342 x1.29

$b=$441.18

Answer:

(x+3)^2 + (y+5)^2 = 36

Step-by-step explanation:

We can write the equation of a circle as

(x-h)^2 + (y-k)^2 = r^2  where (h,k) is the center and r is the radius

(x--3)^2 + (y--5)^2 = 6^2

(x+3)^2 + (y+5)^2 = 36

Answer:

3500

Step-by-step explanation:

multiply 10*350

Answer:

The cash  paid to the bondholder on July 1 is    Z =  $7000

Step-by-step explanation:

From the question we are told that

  The percentage bond issued by the company is [tex]n = 7[/tex]%

    The par value of the bond is [tex]V =[/tex]$200,000

     The market rate is [tex]r = 6[/tex]%

So we are told that the bonds pay interest semiannually on January 1 and July

So the cash  paid to the bondholder on July 1 is mathematically evaluated as

Z =  [tex]V * \frac{7}{100} * \frac{1}{2}[/tex]        

substituting value

   Z =  [tex]200000 * \frac{7}{100} * \frac{1}{2}[/tex]  

      Z =  $7000

Final answer:

The cash paid on July 1 to bondholders for the company's 7% bonds with a par value of $200,000 is $7,000. This is calculated by first determining the annual interest payment and then dividing by two for the semiannual payment.

Explanation:

Understanding Bond Interest Payments

The question revolves around how much cash is paid to bondholders on July 1 for a company that issued 7% bonds with a par value of $200,000 at par when the market rate was 6%. Since the bonds were issued at par, this implies that the bond's stated interest rate matches the market interest rate at the time of issuance. However, the market rate later does not affect the fixed payments of a bond issued at par.

The interest payment for this bond would be calculated using the face value and the stated annual interest rate, which is then divided by two since interest is paid semiannually. The calculation is as follows:

Therefore, the cash paid on July 1 to the bond holder(s) is $7,000.

Answer:

1/4

Step-by-step explanation:

[tex](\dfrac{3(3)^{-2}(-1)^6}{2(3)^{-1}(-1)^5})^2=[/tex]

[tex](\dfrac{\frac{1}{3}}{-\frac{2}{3}})^2=[/tex]

[tex](-\dfrac{1}{2})^2=[/tex]

[tex]\frac{1}{4}[/tex]

Hope this helps!

Answer:

1. Where are the vertical asymptotes on the graph of the secant function?

choice A: x = π /2 + nπ

2. The range of the secant function is

answer:  y ≤  -1  or y ≥  1

3. What is the period of the secant function?

Choice C : 2π

Step-by-step explanation:

there are 3 questions on this page.

correct on edge

The range of secant is  y ≤  -1  or y ≥  1.

The range of a function is the set of its possible output values.

As we know the vertical asymptotes of the secant function

x = π /2 + nπ

and, The range of the secant function is

 y ≤  -1  or y ≥  1

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Answer:

(3^6)/2

Step-by-step explanation:

make sure everything as the numerator is in parenthesis

Answer:

1/ 6^12

Step-by-step explanation:

f[x} = x ^ (-2x)

f(6) = 6 ^ (-2*6)

      = 6 ^ -12

   We know the negative exponent moves it to the denominator

     = 1/ 6^12

Answer:

17.5%

Step-by-step explanation:

Convert fraction (ratio) 7 / 40 Answer: 17.5%

Answer:

17.5

Step-by-step explanation:

7/40 = 17.5

Hope this helps! Please mark brainliest :)

Answer:

81.25

Step-by-step explanation:

45.55 + 35.7

Answer:I hope that helps

Step-by-step explanation:

to get the variable alone you need to add three to both sides

x-3=7

+3  +3

-----------------

x= 10

Answer:

Step 1: Bring like terms together Step 2: Add variable to both sides Step 3: Simplify Step 4: Add the constant to both sides Step 5: Simplify  Step 6: Divide by the coefficient Step 7: Solve Step 8: Test your solution Answer: 10

Step-by-step explanation:

Answer:

  (f◦g)(x) = 6x +9

Step-by-step explanation:

Use g(x) as the argument to f(x) and simplify.

  (f◦g)(x) = f(g(x)) = f(3x +5) = 2(3x +5) -1

  (f◦g)(x) = 6x +9

The surface area of the triangular prism is 171.2 square centimeters.

From the given triangular prism,

Area of base (rectangle) = Length×Breadth

= 8×6=48 square centimeter

So, area of 3 congruent rectangles = 3×48

= 144 square centimeter

Here, area of a triangle = 1/2 × Base × Height

= 1/2 ×6×5.2

= 15.6 square centimeter

So, area of 2 congruent triangles= 2×15.6

= 31.2 square centimeter

Total surface area = 144+31.2

= 171.2 square centimeter

Therefore, the surface area of the triangular prism is 171.2 square centimeters.

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Answer:

A. a rectangle and a triangle

Answer:

a) rectangle and triangle, then add both to fin the total area.

Step-by-step explanation:

Final answer:

The domain of the function y = x^(1/3) (cube root of x) is all real numbers, which is expressed as (-∞, +∞).

Explanation:

The domain of a function describes all the possible values of 'x' for which the function is defined. In the case of the function y = cubic root of x, which is written as y = x^(1/3), the function is defined for all real numbers because you can take the cubic root of any real number, negative, positive, or zero. Hence, the domain of the function y = x^(1/3) is all real numbers, which mathematically is expressed as (-∞, +∞). This is different from the function y = x^2, where the domain must often be restricted to nonnegative numbers to have a well-defined real inverse function.

Answer:

[tex]d = 14,600\,km[/tex]

Step-by-step explanation:

The distanced travelled is equal to twice the distance between points A and B. The distance that was walked in meters is:

[tex]d = 2\cdot (7.3\,km)\cdot \left(\frac{1000\,m}{1\,km} \right)[/tex]

[tex]d = 14,600\,km[/tex]

Final answer:

The total distance walked on the Red Trail, back and forth, when converted from kilometers to meters, is 14,600 meters.

Explanation:

The question asks for the total distance walked in meters if a person walks from point A to point B and back on the Red Trail, where the distance between point A and point B is 7.3 kilometers.

Firstly, we know that 1 kilometer equals 1,000 meters. Therefore, to find the distance in meters for a single trip from point A to point B, we multiply 7.3 kilometers by 1,000:

Since the trip was made back and forth, the total distance covered is twice the distance of a single trip:

Therefore, the total distance walked back and forth on the Red Trail, in meters, is 14,600 meters.

Answer:

x = 45 degrees +180 n  where n is an integer

Step-by-step explanation:

tan(x)-cos^2(x)=sin^2(x)

Add cos^2(x) to each side

tan(x)-cos^2(x)+ cos^2(x)=sin^2(x)+ cos^2(x)

tan(x)=sin^2(x)+ cos^2(x)

We know that sin^2(x)+ cos^2(x) = 1

tan (x) =1

Take the inverse tan of each side

tan ^-1 ( tan x) = tan ^-1 (1)

x = 45 degrees +180 n  where n is an integer

Answer:

Pi/4+kpi

Step-by-step explanation:

X= 45 degrees and on unit circle that is pi/4

Answer:

x = 5/4

Step-by-step explanation:

√2+√2+√2+√2 = 2^x

4√2 = 2^x

4√2 = [tex]2^{\frac{5}{2} }[/tex] = [tex]2^{x}[/tex]

x = 5/2

Answer:

x = 5/4

Step-by-step explanation:

√2+√2+√2+√2 = 2^x

4√2 = 2^x

4√2 =  =

x = 5/2

Answer:

  108

Step-by-step explanation:

"At this rate, ..." means we're to assume Nancy's score is proportional to the number of holes:

  score/18 = 24/4

Multiplying by 18, we get ...

  score = 18(24/4) = 18(6) = 108

Nancy can expect a score of 108 on 18 holes.

Answer:

[tex](a)\dfrac{92}{117}[/tex]

[tex](b)\dfrac{8}{39}[/tex]

[tex](c)\dfrac{25}{117}[/tex]

Step-by-step explanation:

Number of Men, n(M)=24

Number of Women, n(W)=3

Total Sample, n(S)=24+3=27

Since you cannot appoint the same person twice, the probabilities are without replacement.

(a)Probability that both appointees are men.

[tex]P(MM)=\dfrac{24}{27}X \dfrac{23}{26}=\dfrac{552}{702}\\=\dfrac{92}{117}[/tex]

(b)Probability that one man and one woman are appointed.

To find the probability that one man and one woman are appointed, this could happen in two ways.

P(One man and one woman are appointed)[tex]=P(MW)+P(WM)[/tex]

[tex]=(\dfrac{24}{27}X \dfrac{3}{26})+(\dfrac{3}{27}X \dfrac{24}{26})\\=\dfrac{72}{702}+\dfrac{72}{702}\\=\dfrac{144}{702}\\=\dfrac{8}{39}[/tex]

(c)Probability that at least one woman is appointed.

The probability that at least one woman is appointed can occur in three ways.

P(at least one woman is appointed)[tex]=P(MW)+P(WM)+P(WW)[/tex]

[tex]P(WW)=\dfrac{3}{27}X \dfrac{2}{26}=\dfrac{6}{702}[/tex]

In Part B, [tex]P(MW)+P(WM)=\frac{8}{39}[/tex]

Therefore:

[tex]P(MW)+P(WM)+P(WW)=\dfrac{8}{39}+\dfrac{6}{702}\\$P(at least one woman is appointed)=\dfrac{25}{117}[/tex]

Answer:

[tex]\theta = tan^{-1}(\frac{y}{x})[/tex]

Step-by-step explanation:

If we are given components of a vector then we can find the angle between them.

Suppose we are given a vector v

[tex]v = (x, y)[/tex]

Where x is the horizontal component and y is the vertical component.

The angle can be found by using

[tex]tan(\theta)=\frac{y}{x}\\\\\theta = tan^{-1}(\frac{y}{x})[/tex]

The magnitude of the vector v can be found using

[tex]v = \sqrt{x^{2}+y^{2}}[/tex]

Example:

Lets do a quick example:

[tex]v = (2, 4)[/tex]

The angle of the vector is

[tex]tan(\theta)=\frac{4}{2}\\\\\theta = tan^{-1}(\frac{4}{2})\\\\\theta = 63.43^{\circ}[/tex]

The magnitude of the vector is

[tex]v = \sqrt{x^{2}+y^{2}}\\\\v = \sqrt{2^{2}+4^{2}}\\\\v = \sqrt{4+16}\\\\v = \sqrt{20}\\\\v = 4.47[/tex]

Answer:

Simplified as -3 - x

Step-by-step explanation:

I know, you want to simplify this answer.

So.

1 + 2x - 3x - 4 = 1 - x - 4  =  -3 - x

Maria and her friends rides for 56 minutes

Start time = 01:09

End time = 02:05

∴ Ride Time = 60-4

∴ Ride Time = 56 minutes

Therefore the total ride time that Maria and her friend rode is 56 minutes

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Answer:

Step-by-step explanation:

From the given information,

The required correct answers are,

1. The sample is:

b) simple random sample

2. np0 (1-p0) ___ 10

a) greater than or equal to

3. n ___ 0.05N

b) less than or equal to

Hypotheses:

4. H0:p___0.75

d) =

5. H1:p___0.75

a) ≠

6. The test statistic is a

a) z test statistic

7. test statistic=2.8284

8. p-value=0.0047

Decision:

Because p-value less than Alpha=0.05, we reject null hypothesis.

Conclusion:

The data support the claim that the proportion has changed.

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

p = 3/4 = 0.75

For the alternative hypothesis,

p ≠ 0.75

Considering the population proportion, probability of success, p = 0.75

q = probability of failure = 1 - p

q = 1 - 0.75 = 0.25

Considering the sample,

Sample proportion, P = x/n

Where

x = number of success = 480

n = number of samples = 600

P = 480/600 = 0.8

We would determine the test statistic which is the z score

z = (P - p)/√pq/n

z = (0.8 - 0.75)/√(0.75 × 0.25)/480 = 2.53

Recall, population proportion, P = 0.75

The difference between sample proportion and population proportion(P - p) is 0.8 - 0.75 = 0.05

Since the curve is symmetrical and it is a two tailed test, the p for the left tail is 0.75 - 0.05 = 0.7

the p for the right tail is 0.75 + 0.05 = 0.8

These proportions are lower and higher than the null proportion. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area

From the normal distribution table, the area above the test z score in the right tail 1 - 0.9943 = 0.0057

We would double this area to include the area in the left tail of z = - 2.53. Thus

p = 0.0057 × 2 = 0.0114

Because alpha, 0.05 > than the p value, 0.0114, then we would reject the null hypothesis.

Therefore, at 5% significance level, this data provide evidence that the proportion has changed.

Answer: d. Independent Samples T Test

Step-by-step explanation: Independent Samples T Test is commonly used when you want to compare the means of two independent groups and determine if there is evidence that the the associated means are significantly different.

For this test, the data must have: continuous dependent variable; independent variable is categorical (two or more groups); cases that have values on both variables; the obervations are independent, i.e. the groups don't interfere on each other; random sample of data for the population; normal distribution of the dependent variable for each group; homogeneity of variances and no outliers.

Each groups should have at least 6 subjects and have the same number of individuals in each group.

The hypothesis in this test can be expressed as:

H₀: μ1 = μ2 or μ1 - μ2 = 0

H₁: μ1 ≠ μ2 or μ1 - μ2 ≠ 0