Algebra. Solve for x and y.
(11x+34)
(5y-3)
(15x+18)
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Please help !!

Answer:

Step-by-step explanation:

Tom wanted to find the inverse of f(x)= 4x - 2 using the steps in the attached image.

Tom's first mistake was in Step 3.

To correct the mistake, he should not switch the variables.

The correct procedure is:

Step 1 : Given

f(x) = 4x - 2

Step 2 : Change f(x) to y

y = 4x - 2

Step 3 : Add 2 to both sides

\(4x=y+ 2\)

Step 4:  Divide each side by 4

\(x=\dfrac{y+2}{4}\)

Step 5: Change x to \(f^{-1}(x)\)

\(f^{-1}(x)=\dfrac{y+2}{4}\)

Answer:

\(3 \times \frac{1}{3 } + \frac{1}{2} \times - 12( \frac{1}{3} ) = \frac{1}{3} \)

\( - 34 < - 2(4x - 1) \\ - 34 < - 8x + 2 \\ - 34 - 2 < - 8x \\ - 36 < - 8x \\ 36 > 8x \\ \frac{36}{8} > x \\ x < \frac{9}{2} \)

True.

A 95% confidence interval for the population mean means that if we draw multiple samples from the same population and construct confidence intervals for the mean using each sample, then 95% of those intervals will contain the true population mean. This is because the confidence interval is computed based on the sample mean and the sample's standard deviation, which are random variables that are expected to vary from sample to sample. Therefore, we cannot be 100% certain that the true population mean is within any particular confidence interval, but we can be confident (95% confident, in this case) that most of the intervals we construct will contain the true mean. A 95% confidence interval for the population mean implies that if samples are drawn repeatedly and confidence intervals for μ are constructed, then 95% of the confidence intervals computed will contain the population mean. This means that you can be 95% confident that the true population mean lies within the calculated interval.

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Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

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Answer:

(y+2)•(y-6)

Step-by-step explanation:

y(y-6)+2(y-6)

y^2-6y+2y-12

y^2-4y-12

Factors multiply to get a product. You can take this process in reverse.

As another example, the number 12 factors into 3*4, where 3 and 4 are the two factors. This idea applies to both numbers and variable expressions as well.

Answer:

its 113.04

Step-by-step explanation:

took the test

Hi ;-)

\(3w+6w-19=-91\\\\3w+6w=-91+19\\\\9w=-72 \ \ /:9\\\\\huge\boxed{x=-8}\)

Answer:

Step-by-step explanation:

Given:

Isolate w, add 19 to both sides:

Simplify both sides:

Divide both sides by 9:

The mean of the distribution of sample means is 56.7, and the standard deviation of the distribution of sample means is approximately equal to 4.82.

To calculate the mean of the distribution of sample means, we use the fact that the mean of a sample is an unbiased estimate of the population mean, and therefore the mean of the distribution of sample means is equal to the population mean. Thus, the mean of the distribution of sample means is 56.7.

To calculate the standard deviation of the distribution of sample means, we use the formula for the standard error of the mean, which is the population standard deviation divided by the square root of the sample size. Thus, the standard deviation of the distribution of sample means is equal to 75.9 divided by the square root of 246, which is approximately equal to 4.83.

Therefore, the mean of the distribution of sample means is 56.7, and the standard deviation of the distribution of sample means is approximately 4.83

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Answer:

25

Step-by-step explanation:

Given,

Measurement of <1 = x + 10

Measurement of <2 = 4x + 5

Also, said in the question that both these angles are complementary.

Therefore, by the problem,

<1 + <2 = 90°

=> x + 10 + 4x + 5 = 90

=> x + 4x + 10 + 5 = 90

=> 5x + 15 = 90

=> 5x = 90 - 15 = 75

\( = > x = \frac{75}{5} \)

=> x = 15

Now, we have got the value of x so,

Measurement of <1 is

<1 = x + 10 = 15 + 10 = 25 (Ans)

Answer: is 13

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

An estimate for the total number of dragonflies around the lake is 930 by proportional equation.

Let x be the total number of dragonflies around the lake.

We know that on Saturday, Greta caught 120 dragonflies and tagged them.

Therefore, the proportion of tagged dragonflies in the lake is 120/x.

On Sunday, Greta caught 124 dragonflies, and 16 of them were tagged. This means that the proportion of tagged dragonflies in the lake is 16/124.

Since the same proportion of dragonflies were tagged on both days, we can set up an equation:

120/x = 16/124

Solving for x, we get:

x = (120 × 124) / 16 = 930

Therefore, an estimate for the total number of dragonflies around the lake is 930.

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In quadrilateral ABCD, we have: ∠B = 103°, ∠C = 85.67°, and ∠D = 85.67°Now, to find ∠BCD (i.e. ∠BCD), we can use the fact that: ∠B + ∠C + ∠D + ∠BCD = 360°Substituting the given values, we get: ∠B + ∠C + ∠D + ∠BCD = 360°103° + 85.67° + 85.67° + ∠BCD = 360°⇒ ∠BCD = 85.67°.

Given, quadrilateral ABCD with AB || DC and AD || BC. Angle B is 103° and we have to find the measure of angle BCD (i.e. ∠BCD). Let's solve this problem step-by-step:Since AB || DC, the opposite angles ∠A and ∠C will be equal:∠A = ∠C (Alternate angles)We know that, ∠A + ∠B + ∠C + ∠D = 360° Substituting the given values in the above equation, we get:∠A + 103° + ∠C + ∠D = 360°  ⇒ ∠A + ∠C + ∠D = 257°We can now use the above equation and the fact that ∠A = ∠C to find ∠D: ∠A + ∠C + ∠D = 257° ⇒ 2∠A + ∠D = 257°  (∵ ∠A = ∠C)  We also know that, AD || BC. Hence, the opposite angles ∠A and ∠D will be equal: ∠A = ∠D (Alternate angles)Therefore, 2∠A + ∠D = 257°  ⇒ 3∠A = 257°  ⇒ ∠A = 85.67°Now, we can find ∠C by substituting the value of ∠A in the equation: ∠A + ∠C + ∠D = 257° ⇒ 85.67° + ∠C + 85.67° = 257°  (∵ ∠A = ∠D = 85.67°)⇒ ∠C = 85.67°Hence, in quadrilateral ABCD, we have: ∠B = 103°, ∠C = 85.67°, and ∠D = 85.67°Now, to find ∠BCD (i.e. ∠BCD), we can use the fact that: ∠B + ∠C + ∠D + ∠BCD = 360°Substituting the given values, we get: ∠B + ∠C + ∠D + ∠BCD = 360°103° + 85.67° + 85.67° + ∠BCD = 360°⇒ ∠BCD = 85.67°Answer:∠BCD = 85.67°.

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Answer:

A Hercules Beetle is 6.97 inches larger than A ladybug

Step-by-step explanation:

A hercules beetle is 7 inches long while a ladybug is about 0.03 cm long when subtracting these two you will get a grand total of 6.97.

Answer:

y = 7/4x + 8

Step-by-step explanation:

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the first line:

negative reciprocal of -4/7 is 7/4

y-intercept is b in the slope-intercept form:

y = 7/4x + 8

Answer:

1. angle m=angle L

2.MR=RL

3.ang;e O=angle P

Triangle MOR= triangle LPR

ASA

4. angle M= angle D

5. AM=RD

6. MC=DN

Triangle AMC= RDN

by SSA

Step-by-step explanation:

Answer:

1. angle m=angle L

2.MR=RL

3.ang;e O=angle P

Triangle MOR= triangle LPR

ASA

4. angle M= angle D

5. AM=RD

6. MC=DN

Triangle AMC= RDN

by SSA

Answer:

Step-by-step explanation:

3/9 can be a rational number.

Let me show you:

The Answer and/or 1 : 3 or 3 : 9.

Estimates suggest that up to 90% of children with disabilities have some type of nutritional problem.

These children often face unique challenges that can contribute to a higher risk of nutritional deficiencies or imbalances.

Disabilities can affect various aspects of a child's health, including their ability to eat, digest, absorb nutrients, and maintain a healthy weight.

Additionally, certain disabilities may require specific dietary restrictions or specialized nutritional interventions, which can further complicate their nutritional status.

It is crucial to address these nutritional issues and provide appropriate support to ensure the optimal growth and development of children with disabilities.

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The probability of correctly choosing 4 numbers that match 4 randomly selected balls from a bucket of 35 balls is 1/52360.

To calculate the probability of correctly choosing 4 numbers that match 4 randomly selected balls from a bucket of 35 balls with different numbers from 1 to 35, we need to consider the total number of possible outcomes and the number of favorable outcomes.

Total number of possible outcomes:

Since there are 35 balls in the bucket, the total number of possible outcomes is given by the combination formula:

nCr = n! / [(n-r)! * r!]

In this case, we need to choose 4 balls out of 35, so the total number of possible outcomes is:

35C4 = 35! / [(35-4)! * 4!]

Number of favorable outcomes:

We want to choose 4 numbers that match the 4 randomly selected balls. Since there are 4 balls that need to match, we can consider this as choosing all 4 numbers correctly.

There is only 1 way to choose all 4 numbers correctly.

Therefore, the number of favorable outcomes is 1.

Probability:

The probability of an event is given by the formula:

Probability = Number of favorable outcomes / Total number of possible outcomes

In this case, the probability is:

Probability = 1 / 35C4

Now, let's calculate the probability:

35C4 = 35! / [(35-4)! * 4!]

= (35 * 34 * 33 * 32) / (4 * 3 * 2 * 1)

= 52360

Probability = 1 / 52360

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Answer:

y = -5x - 2

Step-by-step explanation:

We have to use slope intercept form which is y = mx + b

mx is the slope and b is the y intercept. Let's start with the y intercept. The y intercept on this graph is -2 so lets see what it looks like to far

y = mx - 2

Next, we find the slope which is -5

y = -5x - 2

Answer:

y=-5x+-2

Step-by-step explanation:

The variables of the test statistic may be determined to be \($s _1$\), \($s _2$\), \($n_ 1, n _2$\), t, which is the t - distribution test statistic, and \($x _1, x _2$\), which is the mean of the two samples.

When the variances of the two groups are not equal, pooled standard deviation estimations cannot be used. As an alternative, we must determine the standard error for each group separately. The variables of the test statistic may be determined to be \($s _1$\), \($s _2$\), \($n_ 1, n _2$\), t, which is the t - distribution test statistic, and \($x _1, x _2$\), which is the mean of the two samples.

The formula for this type of test statistic is given by -

\($t=\frac{x_1-x_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{x_2}{n_2}}}$$\)

Here, the variables can be defined as below -

\($s_1^2, s_2^2=$\) variance of two samples

\($n_1, n_2=$\) respective sizes of the two samples

t = t - distribution test statistic

\($x_1, x_2=$\) Mean of the two samples

As a result, the variables of the test statistic can be determined to be \($s _1, s _2$\), which represents the variance of two samples, \($n _1, n _2$\), which represents the size of the two samples, t, which represents the t-distribution test statistic, and \($x _1, x _2$\), which represents the mean of the two samples.

The complete question is:

The formula for the test statistic used for a two sample test of means where the population variances are unknown and unequal is:

t = X1−X2√s12/n1+s22/n2X1-X2s12/n1+s22/n2

Match the variables to their description.

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Answer:

6(-3)*4(3)*3

-12 *12 *3

-144*3

-432

Answer: -432

Step-by-step explanation:

Answer:Ross can fill the balloon for 0.2 seconds before it pops.

Step-by-step explanation:

Sure thing! Let's calculate the answer to your math problem. The formula to calculate the volume of a sphere is V = (4/3)πr^3, where r is the radius. Since we know that the maximum radius of the balloon is 5 inches, we can calculate the maximum volume of the balloon, which is V = (4/3)π(5)^3 = 523.6 cubic inches.

Now, we need to calculate the time it takes to fill up 523.6 cubic inches of water using a garden hose with a flow rate of 12 gallons per minute. First, we need to convert the volume to gallons, which is 523.6/231 = 2.265 gallons.

Next, we can use the formula: time = volume / flow rate. Plugging in the values, we get time = 2.265 / 12 = 0.189 seconds. Rounded to the nearest tenth of a second, Ross can fill the balloon for 0.2 seconds before it pops. I hope that helps!