Mark's coach told him that he should
practice 8 times over a three week
period. At this rate, how many times will
Mark practice in 9 weeks?

The shortest distance to reach the starting point by Dolores is 2.7 kilometres.

The shortest distance will be the line directly connecting the two points. This will form the right angled triangle and hence can directly be calculated. We will be calculating hypotenuse from Pythagoras theorem.

Distance² = 2.2² + 1.5²

Taking square on Right Hand Side

Distance² = 4.84 + 2.25

Performing addition on Right Hand Side of the equation

Distance² = 7.09

Taking square root on Right Hand Side

Distance = ✓7.09

Distance = 2.7 kilometres

Thus, the shortest distance back to the starting point is 2.7 kilometres.

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Answer:

-1 1/3

Step-by-step explanation:

4-8=-4

-4/3

-1 1/3

Hope this has helped. have a good day.

Answer:

-4/3

Step-by-step explanation:

First solve the numerator

4-8 = -4

Then divide by the denominator

-4/3

The result is -4/3

Answer:

Step-by-step explanation:

5th term is 6 and the 7th term is 48, we know the nth term for a GP is  arn−1

 so let's substitute the given information in that formula for the nth term

ar3=6

  ar6=48

ar6ar3=486

The  a

and  a

cancelout hence we remain with  r3=8

 take a cube root on both sides and we end up having  r=2

Substitute the value of r in any given equation to get the value of a

ar3=6

a(2)3=6

8a=6

a=34

The formula for the nth term of this GP is given by  34(2n−1)

And when you substitute the value of n in the above formula of nth term you will get the following values; 3/4, 3/2, 3, 6…

Solution to the equation 4x+2 = 12 using the change of base formula is x = 1.442114.

The given equation is 4x+2 = 12.

To solve for x using the change of base formula, we need to isolate x on one side of the equation. We start subtracting 2 from LHS and RHS:

4x+2-2 = 12-2

4x = 10

Next, we use the change of base formula, which states log base a of b is equal to log base c of b divided by log base c of a. In this case, we want to find x, which is the exponent that 4 is raised to in order to get 10.

Rewrite equation:

x = log base 4 of 10

Use the change of base formula, we can present this as:

x = \(log base 10 of 10 / log base 10 of 4\)

Simplifying:

x = 1.442114

Solution to the equation 4x+2 = 12 using the change of base formula is x = 1.442114.

In conclusion, using the change of base formula, the answer to the equation 4x+2 = 12 is roughly 1.442114. This method can be used to solve a variety of problems in the sciences, engineering, and financial sectors, as well as exponential and logarithmic equations.

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Answer:

no and yes

Step-by-step explanation:

no to the ,The Night of the spadefoot toad but yes to hatchet to be honest I think everyone read hatchet when they were in 5th grade cuz I know I did and it was pretty good oh yeah who have read the lion,witch and the wardrobe in fifth grade??

Trevor and Kim will be situated 21 kilometers apart from each other at 1:30 PM. They will be separated by a distance of 21 km when the clock strikes 1:30 in the afternoon.

To determine at what time Trevor and Kim will be 21 km apart, we can set up a distance-time equation based on their relative speeds and distances.

Let's assume that t represents the time elapsed in hours since noon. At time t, Trevor would have traveled a distance of 8t km, while Kim would have traveled a distance of 6t km in the opposite direction.

Since they are running in opposite directions, the total distance between them is the sum of the distances they have traveled:

Total distance = 8t + 6t

We want to find the time when this total distance equals 21 km:

8t + 6t = 21

Combining like terms, we have:

14t = 21

To solve for t, we divide both sides of the equation by 14:

t = 21 / 14

Simplifying, we find:

t = 3 / 2

So, they will be 21 km apart after 3/2 hours, which is equivalent to 1 hour and 30 minutes.

Therefore, Trevor and Kim will be 21 km apart at 1:30 PM.

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Answer:

45 min

Step-by-step explanation:

look on z-score table for the value .900

closest on my table is z-score + 1.28

   this is 1.28 S.D. above the mean

          36 + 1.28 * 7 = ~ 45 min

Answer:

105 ft

Step-by-step explanation:

Below sea level : negative

Above sea level : positive

112ft + -7ft = 105 ft

One of the sample t-test significance 0.10 level, we do not reject the null hypothesis that the mean volume of liquid dispensed by the machine is equal to 180 ml.

A one-sample t-test to determine whether the mean volume of liquid dispensed by the machine is significantly different from 180 ml.

The null hypothesis is that the true mean volume of liquid dispensed by the machine is equal to 180 ml, while the alternative hypothesis is that it is not equal to 180 ml.

We can calculate the t-value as follows:

\(t = (179.6 - 180) / (1.3 \sqrt (40)) = -1.385\)

Using a t-distribution table with degrees of freedom (df) = 39 (since we have a sample size of 40 and one parameter estimated), and a significance level of 0.10, we find the critical t-value to be ±1.684.

Since our calculated t-value (-1.385) falls within the acceptance region (-1.684 < t < 1.684), we fail to reject the null hypothesis at the 0.10 significance level.

Sufficient evidence to conclude that the mean volume of liquid dispensed by the machine is significantly different from 180 ml.

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The sum of all the possible values of the hypotenuse is 128.4.

According to the statement

we have given that the Three relatively prime integers are the sides of a right triangle and the smallest leg has length 28.

And we have to Find the sum of all the possible values of the hypotenuse.

So, For this purpose, we know that the

Let us consider a three relatively prime integers which are 29,31,37.

we choose these numbers because we have given that the

the smallest leg has length 28.

And according to the Pythagoras theorem.

we know that the

(Hypotenuse)^2 = (Perpendicular)^2 + (Base)^2

And let the smallest length be a base.

So , Put the values of the perpendicular in this one by one then

so,

(Hypotenuse)^2 = (Perpendicular)^2 + (Base)^2

Here Put perpendicular = 29 and base = 28.

Then

(Hypotenuse)^2 = (29)^2 + (28)^2

(Hypotenuse)^2 = 1625

(Hypotenuse) = 40.31

And then

(Hypotenuse)^2 = (Perpendicular)^2 + (Base)^2

Here Put perpendicular = 31 and base = 28.

Then

(Hypotenuse)^2 = (31)^2 + (28)^2

(Hypotenuse)^2 = 1745

(Hypotenuse) = 41.77

And then

(Hypotenuse)^2 = (Perpendicular)^2 + (Base)^2

Here Put perpendicular = 37 and base = 28.

Then

(Hypotenuse)^2 = (37)^2 + (28)^2

(Hypotenuse)^2 = 2153

(Hypotenuse) = 46.40

And then

The all possible values of the hypotenuse are 40.31, 41.77, 46.40.

And the sum become is 128.4

So, The sum of all the possible values of the hypotenuse is 128.4.

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To show that w is in the subspace of R4 spanned by V1, V2, and V3, we need to find constants c1, c2, and c3 such that:

w = c1V1 + c2V2 + c3V3

We can write this as a matrix equation:

| 1 -4 -9 -4 | | c1 | | -2 |

| 6 3 5 1 | x | c2 | = | -1 |

| 2 4 11 -8 | | c3 | | -1 |

| -15 7 22 -14 | | -2 |

We can solve this system of equations using row reduction:

| 1 -4 -9 -4 | | c1 | | -2 |

| 6 3 5 1 | x | c2 | = | -1 |

| 2 4 11 -8 | | c3 | | -1 |

| -15 7 22 -14 | | -2 |

R2 = R2 - 6R1

R3 = R3 - 2R1

R4 = R4 + 15R1

| 1 -4 -9 -4 | | c1 | | -2 |

| 0 27 59 25 | x | c2 | = | 11 |

| 0 12 29 -16 | | c3 | | 3 |

| 0 -23 67 -59 | | -32 |

R4 = R4 + 23R2

| 1 -4 -9 -4 | | c1 | | -2 |

| 0 27 59 25 | x | c2 | = | 11 |

| 0 12 29 -16 | | c3 | | 3 |

| 0 0 174 -294 | | 225 |

R3 = R3 - (12/27)R2

R4 = (1/174)R4

| 1 -4 -9 -4 | | c1 | | -2 |

| 0 27 59 25 | x | c2 | = | 11 |

| 0 0 -1 22/3 | | c3 | | -13/3 |

| 0 0 1 -98/87 | | 25/58 |

R1 = R1 + 4R3

R2 = R2 - 59R3

R4 = R4 + (98/87)R3

| 1 0 -13 -10/3 | | c1 | | 21/29 |

| 0 27 0 -2119/87 | x | c2 | = | 2238/87 |

| 0 0 1 -98/87 | | c3 | | 25/58 |

| 0 0 0 1390/2391 | | 1009/2391 |

R1 = R1 + (13/1390)R4

R2 = (1/27)R2

R3 = R3 + (98/1390)R4

| 1

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Answer:

1/4

Step-by-step explanation:

distribute the 3/4 through the equation

3/4x + 6 = 9

subtract 6 from both sides

3/4x = 3

divide both sides by 3/4

x= 1/4 or .25

Answer:

x=4

Step-by-step explanation:

Distribute

3/4x+6=9

Subtract

9-6=3

3/4x=3

Divide

3 / 3/4

x=4

The probability of any one undergraduate being selected in a random sample of 2550 undergraduates from a population of 25500 can be calculated using the formula:

Probability = Number of individuals in the sample / Total population

In this case, the probability would be:

Probability = 2550 / 25500 = 0.1 or 10%

Therefore, the probability of any one undergraduate being included in the random sample is 10%. This means that for every 10 undergraduates in the population, only one would be included in the sample. It is important to note that this probability assumes a truly random sampling process with no bias or influencing factors affecting the selection of individuals.

In conclusion, the probability of any undergraduate being in a random sample of 2550 undergraduates selected from a population of 25500 is 10%. This information can be useful in determining the representativeness of the sample and making inferences about the larger population based on the characteristics of the sample.

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Question Completion

Answer:

\((a)120^\circ\\(b)60^\circ\)

Step-by-step explanation:

In the diagram BC(Main Street) is parallel to AD(Willow Lane)

Therefore, ABCD is a Trapezoid.

Since in a trapezoid, adjacent angles are supplementary

Therefore:

\(\angle C+ \angle D=180^\circ\\\angle C+ 60^\circ=180^\circ\\\angle C=180^\circ- 60^\circ\\\angle C=120^\circ\)

Since \(AB \cong CD\), ABCD is an Isosceles Trapezoid.

In an Isosceles trapezoid, the base angles are congruent:  

Therefore:\(\angle A \cong \angle D$ and \angle B \cong \angle C\)

Therefore:

\(\angle A \cong \angle D=60^\circ\\\angle B \cong \angle C=120^\circ\)

(a)

The angle between Main Street and the west path is \(\angle CBA = 120^\circ\)

(b)

The angle between the west path and Willow Lane is \(\angle BAD =60^\circ\)

Answer:

-5

Hope this helps!

Answer:

c

Step-by-step explanation:

Answer:

Blue: 2/8

Red or Yellow: 3/8

Not Brown: 8/8

Not Green: 5/8

Number Five: 20%

Step-by-step explanation:

First Four Questions: See how many parts the spinner is in then count the number of colors its asking or not asking for and put that number over the total amount of parts

Question Five: If it shows up on time 80 percent of the time then the other 20 percent of the time they were late so there is a 20 percent chance of that happening again.

Answer:

the answer is X

X^(m-3) ÷ X^(m-4).

( for division you subtract in indices)

= X^(m-3)-(m-4)

Note: open the bracket with the the minus sign

=X^(m-3-m+4)

= collect the like terms X^(m-m-3+4)

= X^(0+1)

=X^1

=X

Answer:

chord

Step-by-step explanation:

A chord of a circle is a straight line segment whose endpoints both lie on a circular arc

To determine if a majority of the citizens felt that the country could develop a way to protect itself from atomic bombs in 1945, we can perform a hypothesis test using the provided data and a significance level of 0.05 (alpha = 0.05).

Let's set up the hypotheses:

Null Hypothesis (H0): The proportion of citizens who felt the country could develop a way to protect itself from atomic bombs is equal to or less than 0.5 (no majority).

Alternative Hypothesis (H1): The proportion of citizens who felt the country could develop a way to protect itself from atomic bombs is greater than 0.5 (a majority).

We can use the one-sample proportion test to evaluate the null hypothesis. The test statistic used is the z-test statistic.

Next, we calculate the test statistic:

Sample proportion (p) = 752 / 1453 = 0.5179

Standard Error (SE) = sqrt((0.5 * 0.5) / 1453) = 0.0155

Now, we calculate the z-score:

z = (p - p) / SE = (0.5179 - 0.5) / 0.0155 = 1.129

Using a standard normal distribution table or a calculator, we can find the critical value corresponding to a significance level of 0.05. For a one-tailed test, the critical value is approximately 1.645.

Since the test statistic (1.129) is less than the critical value (1.645), we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that a majority of the citizens felt the country could develop a way to protect itself from atomic bombs in 1945 at a significance level of 0.05.

Therefore, based on the given data and the hypothesis test, we cannot conclude that a majority of the citizens felt the country could develop a way to protect itself from atomic bombs in 1945.

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The probability of selecting either lunch is 50%, as both lunches are equally likely to be chosen. This is because both lunches have the same ingredients, with the only difference being the dessert item.

Probability is a measure of the likelihood of a certain event or outcome occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event or outcome is impossible and 1 indicates that the event or outcome is certain to occur. Probability is an important concept in mathematics and statistics, and it is widely used in fields such as finance, science, engineering, and gaming.

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Answer:

∴ The other integer is -2099.

Step-by-step explanation:
Let the unknown number be x,

599+x=(-1500)

x=(-1500)-599

x=(-2099)

The value of the triple integral is 72π.

To evaluate this triple integral in cylindrical coordinates, we first need to express the region E using cylindrical coordinates.

The cylinder x² + y² = 16 can be expressed in cylindrical coordinates as r² = 16, or r = 4. The planes z = -5 and z = 4 define a region of height 9.

So, the region E can be expressed in cylindrical coordinates as:

4 ≤ r ≤ 4

-5 ≤ z ≤ 4

0 ≤ θ ≤ 2π

The integrand √(x² + y²) can be expressed in cylindrical coordinates as r, so the integral becomes:

∭E√x²+y²dV = ∫0²π ∫4⁴ ∫-5⁴ r dz dr dθ

Note that the limits of integration for r are from 0 to 4, which means we are only integrating over the positive x-axis. Since the integrand is an even function of x and y, we can multiply the result by 2 to get the total volume.

The integral with respect to z is easy to evaluate:

∫₋₅⁴ r dz = r(4 - (-5))

= 9r

So the triple integral becomes:

∭E√x²+y²dV = 2 ∫0^2π ∫4⁴ 9r dr dθ

= 2(9) ∫0^²π 4 dθ

= 72π

Therefore, the value of the triple integral is 72π.

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Answer:

Step-by-step explanation:

a) The critical t-values are approximately -3.182 and +3.182.

b) If a type I error is committed in this test, it means that the null hypothesis (H₀) is incorrectly rejected when it is actually true.

Here, we have,

a) To perform a test of significance to determine whether the mean amount of juice dispensed is different from 12.1 fluid ounces at =0.05, we can follow these steps:

Given:

Sample mean (x) = 12.05 fluid ounces

Standard deviation (s) = 0.085 ounce

Sample size (n) = 4

Population mean (μ) = 12.1 fluid ounces

Step 1: State the hypotheses.

Null hypothesis (H₀): The mean amount of juice dispensed is equal to 12.1 fluid ounces. (μ = 12.1)

Alternative hypothesis (H₁): The mean amount of juice dispensed is different from 12.1 fluid ounces. (μ ≠ 12.1)

Step 2: Select a significance level.

The significance level (α) is given as 0.05.

Step 3: Compute the test statistic.

Since the population standard deviation is unknown and the sample size is small (n < 30), we'll use a t-test.

The formula for the t-test statistic is:

t = (x - μ) / (s / √n)

Plugging in the values:

t = (12.05 - 12.1) / (0.085 / √4)

Step 4: Determine the critical value.

Since it's a two-tailed test and α = 0.05, we divide the significance level by 2 to get α/2 = 0.025.

The degrees of freedom (df) for a sample size of 4 is n - 1 = 3.

We can find the critical t-values using a t-table or a t-distribution calculator.

For α/2 = 0.025 and df = 3,

the critical t-values are approximately -3.182 and +3.182.

Step 5: Make a decision.

If the calculated t-value falls within the critical region (beyond the critical t-values), we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

Step 6: Calculate the p-value.

Alternatively, we can calculate the p-value associated with the t-value and compare it to the significance level. If the p-value is less than the significance level (0.05), we reject the null hypothesis.

Without the specific values for the mean, standard deviation, and sample size, it is not possible to perform the calculations required for Steps 3-6. Please provide those values, and I can help you complete the test of significance.

b) If a type I error is committed in this test, it means that the null hypothesis (H₀) is incorrectly rejected when it is actually true. In the context of the situation, this would lead to the machine being shut down for recalibration even though there is no convincing evidence that the mean amount of juice dispensed is different from 12.1 fluid ounces. It would result in unnecessary machine downtime and potential costs for recalibration.

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complete question:

A bottle-filling machine is set to dispense 12.1 fluid ounces into juice bottles. To ensure that the machine is filling accurately, every hour a worker randomly selects four bottles filled by the machine during thepast hour and measures the contents. If there is convincing evidence that the mean amount of juice dispensed is different from 12.1 ounces, the machine is shut down for recalibration. It can be assumed that the amount of juice that is dispensed into bottles is normally distributed. During one hour, the mean number of fluid ounces of four randomly selected bottles was 12.05 and the standard deviation was 0.085 ounces.

a) Perform a test of significance to determine whether the mean amount of juice dispensed is different from 12.1 fluid ouncesat=0.05.

b) Suppose you commit a type I error in this test, what would be a logical consequence of the machine given the context of the situation?

You should invest $22,627.84 if you want to receive payments of $3,000 at the end of each year for 10 years, with the first payment 3 years from now, if the money is compounded at 5% annually.

To solve this problem, we can use the present value formula for an ordinary annuity: PV = PMT * [1 - (1 + r)^-n] / r

Where:

PV = present value

PMT = periodic payment

r = interest rate

n = number of payments

In this case, we have:

PV = unknown

PMT = $3,000

r = 5%

n = 10 years (first payment in 3 years, so there are 10 payments after that)

Plugging these values into the formula,

we get:

PV = $3,000 * [1 - (1 + 0.05)^-10] / 0.05

PV = $22,627.84

Therefore, you should invest $22,627.84 if you want to receive payments of $3,000 at the end of each year for 10 years, with the first payment 3 years from now, if the money is compounded at 5% annually.

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Answer: 8x^2 + 55x + 42

Step-by-step explanation:

(x+6)(8x+7)=

(8x*x)+(7x)+(6*8x)+(6*7)=

8x^2 + 7x + 48x + 42=8x^2 + 55x + 42

The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.

M₁ = 35

M₂ = 45

SM1-M2 = 6.00

The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers. To calculate the t-value, the formula we need to use here is:

t = (M₁ - M₂) / SM1-M2

Substituting the given values into the formula:

t = (35 - 45) / 6.00

t = -10 / 6.00

t = -1.67

Therefore, we can conclude that the value of t is -1.67 for the samples given.

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The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.

Given, M₁ = 35

M₂ = 45

SM1-M2 = 6.00

The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers.

To calculate the t-value,

the formula we need to use here is:

t = (M₁ - M₂) / SM1-M2

Substituting the given values into the formula:

t = (35 - 45) / 6.00

t = -10 / 6.00

t = -1.67

Therefore, we can conclude that the value of t is -1.67 for the samples given.

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The matrix a for which av is the orthogonal projection of v onto the plane 2x y − 2z = 0 is [(2/3) (1/3) (-√3/3); (1/3) (2/3) (√3/3); (-√3/3) (√3/3) (2/3)].

Let's first find a vector that is normal to the plane 2x + y - 2z = 0. We can do this by finding two vectors that lie in the plane and then computing their cross-product.

Letting x = 1, y = 0, and z = 1, we get the point (1, 0, 1) which is in the plane. Letting x = 0, y = 2, and z = 1, we get the point (0, 2, 1) which is likewise in the plane.

The vector between these two focuses is (1, 2, 0), and a type to the plane is given by taking the cross result of this vector with the vector (2, 1, - 2) which is a vector lined up with the plane.

Utilizing the cross-item recipe, we have:

n = (1, 2, 0) × (2, 1, - 2) = (- 4, 4, - 4)

We can standardize n to get a unit vector that is typical to the plane:

n = (- 4/√12, 4/√12, - 4/√12) = (- √3/3, √3/3, - √3/3)

To find the matrix a, we use the formula for the projection of a vector v onto a plane with normal vector n:

proj_n(v) = v - (v · n)n

where v · n is the dot product of v and n.

Letting v = (x, y, z), we have:

proj_n(v) = (x, y, z) - ((x, y, z) · (- √3/3, √3/3, - √3/3))(- √3/3, √3/3, - √3/3)

= (x, y, z) - ((- √3x + √3y - √3z)/3)(- √3/3, √3/3, - √3/3)

= (x, y, z) + ((√3x - √3y + √3z)/3)(- √3/3, √3/3, - √3/3)

Therefore, the matrix a is given by:

a = I - proj_n

= I - [(√3/3) (-√3/3) (-√3/3); (√3/3) (-√3/3) (√3/3); (-√3/3) (-√3/3) (-√3/3)]

= [(2/3) (1/3) (-√3/3); (1/3) (2/3) (√3/3); (-√3/3) (√3/3) (2/3)]

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Given:

The next step to simplify this expression is to distribute the multiplication on the parentheses term. This means that you have to multiply each term inside the parentheses by 7