Part A

Part B
Write an equation for a rational function with: Vertical asymptotes at \( x=1 \) and \( x=-3 \) \( x \)-intercepts at \( x=-6 \) and \( x=6 \) \( y \)-intercept at 7
Write an equation for a rational

Answer:

Will you help me plz I will follow you

Answer:

5/24 of a bag I just had this question an thought I'd help you

Steps to solve:

-7x - 5y = -68 when x = -6

~Substitute and simplify

-7(-6) - 5y = -68

42 - 5y = -68

~Subtract 42 to both sides

-5y = -110

~Divide -5 to both sides

y = 22

Best of Luck!

Answer:

2.37x + 2.58y + 3.49z

Step-by-step explanation:

The expression would be

Let us assume the organges be x

Soup be y

And, the cereal be z

Their cost would be $0.79, $1.29 and $3.49 respectively

Now as per the question

the expression would be

= 0.79 × 3x + 1.29 × 2y + 3.49 × z

= 2.37x + 2.58y + 3.49z

Answer:

x > 20 and x < 50; Malcolm needs to consume more than 20 grams of carbohydrates, but less than 50 grams of carbohydrates.

Step-by-step explanation:

Answer:

the answer is 80 cubic cm.

Step-by-step explanation:

it is simply height X width so 20 X 4= 80 meaning the answer is 80 cm

Answer:

2574

Step-by-step explanation:

Answer:

the answer is =2574

Step-by-step explanation:

hoped I helped:)

Answer:

432? I cannot tell if x is multiplication or a variable

Step-by-step explanation:

Answer:

6*18=108

18*12=216

36*15=540 so 216+540 addition first then subtracting so 215+540=755-180=575

b. be rejected. Since 2.3 > 1.69, we reject the null hypothesis.

Explanation:
We can use a one-sample t-test to determine whether the sample mean differs significantly from the hypothesized population mean of 20.
The test statistic is calculated as follows:
t = (sample mean - hypothesized mean) / (standard error of the mean)
The standard error of the mean is calculated as S / sqrt(n), where S is the standard deviation of the sample and n is the sample size.
Plugging in the values given in the question:
t = (36 - 20) / (12 / sqrt(24.6)) = 6.072
Using a t-table with 23 degrees of freedom (n-1), we find that the critical value for a one-tailed test at 95% confidence is 1.714.
Since our calculated t-value (6.072) is greater than the critical value (1.714), we reject the null hypothesis and conclude that the sample mean is significantly greater than 20 at the 95% confidence level. Since 2.3 > 1.69, we reject the null hypothesis. So, the correct answer is: b. be rejected.

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The LP problem is to maximize the objective function 10x+15y subject to the constraints 2x+5y ≤ 40 and 6x+3y ≤ 48. By graphing the constraints and identifying the feasible region, we can determine the optimal solution.

To find the optimal solution for the LP problem, we first graph the constraints 2x+5y ≤ 40 and 6x+3y ≤ 48. These constraints represent the inequalities that the variables x and y must satisfy. We plot the lines 2x+5y = 40 and 6x+3y = 48 on a graph and shade the region that satisfies both constraints.

The feasible region is the area where the shaded regions of both inequalities overlap. We then identify the corner points of the feasible region, which represent the extreme points where the objective function can be maximized.

Next, we evaluate the objective function 10x+15y at each corner point of the feasible region. The point that gives the highest value for the objective function is the optimal solution.

By solving the LP problem graphically, we can determine the corner point that maximizes the objective function. The optimal solution will have specific values for x and y that satisfy the constraints and maximize the objective function 10x+15y.

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\( \: \: \: \: \: \)

\( = - 4 {x}^{2} \)

refer to the attachment

=> -2x × 2x

=> -4x²

Answer:

x = 7

Step-by-step explanation:

It will be written as 80 = 12x - 4

80=12x−4

Step 1: Flip the equation.

12x−4=80

Step 2: Add 4 to both sides.

12x−4+4=80+4

12x=84

Step 3: Divide both sides by 12.

12x/12 = 84/12

x=7

Answer:

x = 7

Step-by-step explanation:

The circumference of a circle with a diameter of 36 inches is approximately 113.1 inches.

The circumference of a circle can be found using the formula: C = πd, where C represents the circumference and d represents the diameter. In this case, the given diameter is 36 inches.

Using the value of π (pi) as approximately 3.14159, we can substitute the values into the formula:

C = πd

C = 3.14159 * 36

C ≈ 113.09724

Rounding to the nearest tenth, the circumference of the 36-inch diameter circle is approximately 113.1 inches.

The circumference of a circle with a diameter of 36 inches is approximately 113.1 inches.

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785·20%=157

785-157=628

Answer:

You will pay $628 for a item with original price of $785 when discounted 20%. In this example, if you buy an item at $785 with 20% discount, you will pay 785 - 157 = 628 dollars.

(a) Is this an observational study or an experiment?

ans=Observational study – no treatment was imposed

(b) What are the explanatory and response variables?

ans=explanatory – time spent in child care from birth to age 4 response – adult rating of children’s behavior

d) Does this study show that child care causes children to be more aggressive? Explain.

No. Observational studies cannot show cause-and-effect

Researchers=someone whose job is to study a subject carefully, especially in order to discover new information or understand the subject better: She is a leading researcher in the field.

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To graph an inequality y ≥ 3x - 1, first graph a line for y = 3x - 1, and then shad  upward on the y-axis, as given the ≥ sign, check the attatchment.

Equations in mathematics are not always balanced on both sides with a "equal to" symbol. It can occasionally refer to a "not equal to" relationship, where one thing is greater than the other or less than.

A relationship that compares two numbers or other mathematical expressions in an unequal way is referred to as an inequality in mathematics. These mathematical expressions are classified as inequalities in the algebraic language.

To say that two things are not equal is to use the word "inequality." A particular thing could be greater than >, less than <, equal to ≤ or less than or equal to or greater than ≥ the other things.

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If the test statistic value falls within the critical region, we reject the null hypothesis (H0) at the given significance level (α).

If the test statistic value falls outside the critical region, we do not reject the null hypothesis.

To determine the decision regarding the null hypothesis based on a test statistic value and a critical region, we need to compare the test statistic value to the critical value(s) of the test.

Since the question does not provide information about the significance level or the directionality of the test, we cannot determine the critical region or make a decision about the null hypothesis based on the test statistic value alone.

More information is needed to interpret the result of the test.

At the specified significance level (), we reject the null hypothesis (H0) if the test statistic value is inside the crucial zone.

If the test statistic result is outside of the acceptable range, the null hypothesis is not rejected.

The test statistic value to the test's critical value(s) in order to decide whether to reject the null hypothesis based on a test statistic value and a crucial area.

We cannot establish the crucial area or choose the null hypothesis based only on the test statistic value since the question does not specify the significance level or directionality of the test.

To understand the test's outcome, more details are required.

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The graph of the scenario of the inequality 8x + 5y ≤ 100 is added as an attachment

From the question, the given parameters are:

Also, we have the inequality of the possible combinations to be

8x + 5y ≤ 100

Such that

The next step is to plot the graph of the inequality

This can be done by the use of a graphing tool

So, we enter the inequality on the graphing tool and attach the graph

Recall that the inequality is given as

8x + 5y ≤ 100

See attachment for the graph of the inequality 8x + 5y ≤ 100

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Answer:

10

Step-by-step explanation:

To find out how many students participate in both sports and music, we can use the formula:

Total = Group A + Group B - Both

where "Total" is the total number of students participating in sports or music, "Group A" is the number of students participating in sports, "Group B" is the number of students participating in music, and "Both" is the number of students participating in both.

Plugging in the given values, we get:

Total = 100

Group A = 60

Group B = 50

Both = ?

100 = 60 + 50 - Both

Simplifying the equation, we get:

Both = 60 + 50 - 100

Both = 10

Therefore, 10 students participate in both sports and music.

Based on the information provided, the research study is likely to receive the designation of "Well-designed randomized controlled trial" according to the What Works Clearinghouse (WWC) Standards.

Random assignment, low attrition, and minimal confounding variables are key criteria for a well-designed study. Random assignment ensures that participants are assigned to different groups in a random and unbiased manner, minimizing potential selection bias. Low attrition refers to a low dropout rate among participants, which helps maintain the integrity of the study's findings. Minimal confounding variables indicate that the researchers have taken measures to control and reduce the influence of extraneous factors that could impact the study's results.

By meeting these criteria, the research study aligns with the standards of a well-designed randomized controlled trial, which is considered a rigorous and reliable research design for evaluating the effectiveness of interventions or treatments.

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Answer:

When x = 0, the value of f(x) is -3

Each time x increases by 1, f(x) increases by 2

f(x) = 2x - 3

Step-by-step explanation:

✔️From the graph given, values of x is plotted in the horizontal axis while values of f(x) is plotted on the vertical axis.

Thus:

When x = 0, the value of f(x) is -3. => (0, -3)

✔️Each time x increases by 1, f(x) increases by 2. i.e. when x increases from 3 to 4 on the y axis, f(x) increases from 3 to 5 on the why axis.

✔️The equation that models the function can he written in the form of f(x) = ax + b, where:

a = rate of change = rise/run

b = y-intercept = the point on the y-axis that the line intercepts.

Rate of change between the two points on the line (0, -3) and (4, 5):

Rate of change (a) = rise/run = (5 - (-3))/(4 - 0) = 8/4

a = 2

b = y-intercept = -3

✅To write the equation, substitute a = 2 and b = -3 into f(x) = ax + b:

f(x) = 2x + (-3)

f(x) = 2x - 3

Answer:

The answer is "\(\int e^{ax}\ dx=\frac{e^{ax}}{a}+c\)".

Step-by-step explanation:

Please find the complete question in the attached file.

\(\int^{m}_{a}\ f(x)\ dx=\frac{1}{2}\\\\f(x)=ke^{-kx}, \ [0, \infty]\\\\\)

let m is the median

\(so,\\\\ \int^{m}_{a}\ f(x)\ dx=\frac{1}{2}\\\\\to \int^m_0 k\cdot e^{-kx}=\frac{1}{2}\\\\\to [\frac{k\cdot e^{-kx}}{-k}]^m_0=\frac{1}{2}\\\\\to [- e^{-kx}]^m_0=\frac{1}{2}\\\\\to - e^{-km} +1=\frac{1}{2}\\\\\to e^{-km} =\frac{1}{2}\\\\\to e^{km} =2\\\\\to \ln(e^{km}) =\ln 2\\\\\to km= \ln \ 2\\\\\to m=\frac{\ln \ 2}{k}\\\\ \text{the answer is: } \\\\ \to \int e^{ax}\ dx=\frac{e^{ax}}{a}+c\)

Best represents the constant rate at which cupcakes are sold at the bake sale $0. 55 per cupcake

Mrs. Campos is making cupcakes for a bake sale. She uses the equation c = 0. 55x to determine the cost, c, for x cupcakes. Which best represents the constant rate at which cupcakes are sold at the bake sale?

55 cupcakes per dollar

$0. 55 per cupcake

$4 per cupcake

c = 0. 55x

to determine the cost, c,

for x cupcakes.

CASE 1

55 cupcakes per dollar

therefor x = 55

c = 0. 55x

c = 0. 55 × 55

 = 30.25

case2

$0. 55 per cupcake

x = 1

c = 0. 55x

c = 0. 55 × 1

   =  0. 55

case 3

$4 per cupcake

x = 1

c = 0. 55x

c = 0. 55 × 1

   =  0. 55

therefor conclusion is best represents the constant rate at which cupcakes are sold at the bake sale $0. 55 per cupcake

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The profit function is: 40Q - 350000

The break even point in terms of quantity is: 8750

Break even Revenue is: 875000

Determine the total cost of all purchased units.

Divide the total cost by the number of units purchased to get the cost. Calculate the final price using the sales price formula.

Selling price = cost + profit margin.

As par given that sales =25,000

Selling price =br .100

TVC = br 1500000

T F C=b r 350,000. then

Revenue = 25000 * br. 100

Revenue = br 2500000

cost = T V C + TFC

Cost = br. 1850000

Thus:

Profit = Revenue - Cost

Profit = 2500000 - 1850000

Profit = br. 650000

1) TR = QSp = 100Q

TC= TVC + TFC

TVC= (VC)Q= 1,500,000

VC * 250000 = 1500000

VC =  6O

TC= 60Q + 350000

Profit= Q(Sp - Vc) - Fc

(100 - 60)Q - 350000

40Q - 350000

2. BEq = FC/SP - Vc

= 350000/40

= 8750

4. Break even Revenue = BeQ * Sp = 8750* 100=875000

5. Sales volume = profit + TC= 500000 + 1,850,000= 2350000

Quantity of sales = sale volume / Sp = 2350000/100= 23500

6. Profit = sales - Tc = 2,000,000- 1850000=150,000

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(a) The geodesic curvature of a longitude on the unit sphere is 1. (b) The holonomy along the longitude is 2π.

(a) The geodesic curvature of a curve on a surface measures how much the curve deviates from a geodesic. For a longitude on the unit sphere, the geodesic curvature is 1. This is because a longitude is a curve that circles around the sphere, and it follows a geodesic path along a meridian, which has zero curvature, while deviating by a constant distance from the meridian.

(b) Holonomy is a concept that measures the change in orientation or position of a vector after it is parallel transported along a closed curve. For the longitude on the unit sphere, the holonomy is 2π. This means that after a vector is parallel transported along the longitude, it returns to its original position but with a rotation of 2π (a full revolution) in the tangent space. This is due to the nontrivial topology of the sphere, which leads to nontrivial holonomy.

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Answer: 78x

Step-by-step explanation:

Considering the expression of a line, the slope of the line that passes through the points (2,4) and (9,12) is 8/7.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope of the line is calculated as:

m= (y₂ - y₁)÷ (x₂ - x₁)

In this case, being (x₁, y₁)= (2,4) and (x₂, y₂)= (9,12), the slope m can be calculated as:

m= (12 -4)÷ (9 -2)

Solving:

m= 8÷ 7= 8/7

Finally, the slope of the line is 8/7.

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Answer:

the true statement is D. sin A = cos C

it's because,

statements A and B do not match and as for statement C, angle B is not included in trigonometric ratios

They are all true None are false

Answer:

Jenny wants to work out the area of

the trapezium.

13 m

She writes:

13 m

N

12 m

area =-

Step-by-step explanation:

Answer:

The p-value you would use to test the claim

p -value = 0.007

Step-by-step explanation:

Step(i):-

Given random sample size 'n' = 45

Mean of the Population = 18.0 c.m

Standard deviation of the Population(S.D) = 0.25 c.m

Mean of the sample = 17.9 c.m

Null hypothesis :-

               H₀ : μ = 18.0 c.m

Alternative Hypothesis:

             H₁ :  μ ≠ 18.0 c.m

Test statistic

  \(Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }\)

 \(Z = \frac{17.9-18 }{\frac{0.25}{\sqrt{45} } } = -2.688\)

|Z| = |-2.688|

|Z| = 2.688≅ 2.7

Step(ii):-

P -value :-

The z-test statistic value = 2.7

P( Z>2.7) = 1- P(Z< 2.7)

                  = 1- ( 0.5+ A(2.7))

                  = 0.5 - A(2.7)

                  = 0.5 - 0.4965

                 = 0.0035

P( Z>2.688)= 0.0035

Given data is two tailed test

2 X P( Z>2.688) = 2 X 0.035 = 0.007

P-value = 0.007

we will choose level of significance ∝=0.05

P -value < 0.05

H₀ is rejected

Alternative Hypothesis is accepted

Final answer:-

The population mean of  pencils produced in that factory have a mean length is not equal to 18.0 cm.​