A street light is mounted at the top of a 12 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 8 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 35 ft from the base of the pole

Answer:

x = 21/5 or x = -2

Step-by-step explanation:

Answer: See explanation

Step-by-step explanation:

a. Predict the sales resulting from a $15,000 investment in inventory and an advertising budget of $10,000.

To solve this, in the regression equation, we have to replace x1 with 15 and then replace x2 with 10. This will be:

y = 25 + 10x1 + 8x2.

y = 25 + 10(15) + 8(10)

y = 25 + 150 + 80

y = 255

Therefore, the predicted sales is 255.

b. Interpret b1 and b2 in this estimated regression equation.

A change in b1 which is the inventory investment will bring about a change of 10 units in the sales as long as other values are constant.

A change in b2 which is the Advertising expenditure will bring about a change of 8 units in the sales as long as other values are constant.

Answer:

10/4 equals 2 1/2 when simplified.

Step-by-step explanation:

10/4 = 2 2/4 or 2 1/2 when simplified.

This is because, 4 x 2 = 8, and 8 + 2 (or 1/2 of 4) = 10.

Hope this helps! :D

The rate of change in the total amount charged with respect to the time spent on the service call is $40 per hour.

The mathematical concept of rate of change describes how much one quantity changes in relation to another. It is calculated as the difference between the change in the output (the dependent variable) and the change in the input (independent variable).

The rate of change, in other words, informs us of how quickly or slowly something is changing through time or in relation to another variable. When tracking the distance an automobile travels over time, for instance, the rate of change would be the car's speed, which is calculated as the distance traveled divided by the time required.

Slope, which is the ratio of the vertical change (rise) to the horizontal change (run) between two points on a graph, is a common way to depict the rate of change. The rate of change of the dependent variable with respect to the independent variable is depicted by the slope of a straight-line graph.

The rate of change in the total amount charged with respect to the time spent on the service call represents the slope of the graph. We can find the slope of the graph by taking any two points on the line and calculating the change in y (total amount) divided by the change in x (time spent on the service call).

Looking at the graph, we can choose two points: (2, 130) and (8, 370). The change in y is:

370 - 130 = 240

And the change in x is:

8 - 2 = 6

Therefore, the slope (rate of change) of the graph is:

240/6 = 40

So the rate of change in the total amount charged with respect to the time spent on the service call is $40 per hour.

Therefore, the correct option is $40 per hour.

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Answer:

12

Step-by-step explanation:

Given that,

f(x) = 2x² - 3x + 7

To find the value of f ( 2.5 ), replace x with 2.5 and solve the equation.

Let us solve it now.

f(2.5) = 2(2.5)² - 3×2.5 + 7

f(2.5) = 12.5 - 7.5 + 7

f(2.5) = 12

Answer:

\(f(x) = 2 {x}^{2} - 3x + 7 \\ f(2.5) = 2 {(2.5)}^{2} - 3(2.5) + 7 \\ f(2.5) = 12.5 - 7.5 + 7 \\ \boxed{f(2.5) = 12}\)

Answer:

12.5 or 12 1/2 (may be wrong)

Step-by-step explanation:

First I set up a formula to solve how many ounces of salt there were out of 30,      

x/30=20/100, I crossed multiplied and got 5/30, next, I set up the same formula for how many ounces of salt there were out of 25, x/25=30/100, I got 7.5, the last thing I did was add them both together leading me to the answer 12.5 or 12 1/2. Hope this helps! Please say if I am wrong.

Answer:

779 kg

Step-by-step explanation:

5,000 g = 5 kg, 784 - 5 = 779

By taking a quotient between correspondent side lengths, we will see that the scale factor of the dilation applied to the quadrilateral is S = 4.

The scale factor of the dilation is given by the quotient between the length of one of the sides of the dilated figure and the length of the correspondent side of the original figure.

Here the original figure is the smaller quadrilateral, and the dilated figure is the larger one

If we select the top side, the length on the dilated figure is 72 inches, and the length of that side on the original figure is 18 inches, then the scale factor of the dilation is given by:

S = 72in/18in = 4

The scale factor of the dilation is 4.

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Answer:

Correct Answer is 1 Only 5 x 2 5x2 is the second-degree term. Hence, the correct option is (1)

note :

hope i helped

Answer:

Step-by-step explanation:

Has on the scale

Added

Total

Answer:

the total weight is 2550 grams

Step-by-step explanation:

2 1/2 kilograms=5/2×1000grams=2500grams

if 50 grams is added

total weight in grams =2500grams+50grams=2550grams

Answer:

2009000

Step-by-step explanation:

Comparate velocity and time

Magnitudes operations

Part a) How fast ( velocity) was car traveling

V = 12 miles/ 0.2 hours = 12/ (2/10) = 12 x 10 / 2 = 120/2 = 60 miles/hour

Part b). How long ( Time)) did take to travel 204.75 miles

Distance = Velocity x Time

Time = Velocity/ Distance = 60 (miles/hour)/ 204.75( miles) = 0.293 Hours

Time = 0.293 hours = 18 minutes

Standard notation: 329.01

In standard notation, the digits are read from left to right, and each digit represents a different place value. The first digit, 3, represents the hundreds place, the second digit, 2, represents the tens place, the third digit, 9, represents the ones place, the fourth digit, 0, represents the tenths place and the fifth digit, 1, represents the hundredths place.

3100 + 210 + 91 + 00.1 + 1*0.01 = 329 + 20 + 9 + 0 + 0.01 = 329.01

Scientific notation: 3.2901 x 10^2

In scientific notation, the number is written as a decimal number multiplied by a power of 10. The decimal number, 3.2901, represents the coefficient and the power of 10, 10^2, represents the exponent.

3.2901 x 10^2 = 3.2901 x 100 = 329.01

Expanded notation: 3100 + 210 + 91 + 00.1 + 10.01

In expanded notation, the number is written as the sum of each digit multiplied by its corresponding place value.

3100 + 210 + 91 + 00.1 + 10.01 = 329 + 20 + 9 + 0 + 0.01 = 329.01

Fractional notation: 32901/10000

In fractional notation, the number is written as a ratio of two integers. The numerator represents the value of the number, and the denominator represents the place value of the last digit.

32901/10000 = 329.01

Decimal notation: 32901 in base 10

In decimal notation, the number is written as a whole number in base 10. The number can be represented as a combination of digits ranging from 0 to 9.

32901 = 329.01

All the 5 different ways of representation are mathematically equivalent and represent the same number 329.01, they are all different ways of expressing the same value and they all show the understanding of the place value system.

The length of the guy wire to the nearest foot would be = 10 ft.

The relationship between the tower, guy wire and pole forms the shape of a right angle triangle.

The distance from the stake to the pole (opposite) =a = 5 ft

The distance from the pole to the tower (adjacent) =b= 9ft

The length of the guy wire= c = X

Using the Pythagorean formula:

c² = a² + b²

c² = 5² + 9²

c² = 25+81

c² = 106

C = √106

C= 10 ft ( to the nearest foot)

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Complete question:

A guy wire runs from the top of a cell tower to a metal stake in the ground. Sophie places a 7 ft tall pole to support the guy wire. After placing the pole, Sophie measures the distance from the stake to the pole to be 5 ft. She then measures the distance from the pole to the tower to be 9 ft. Find the length of the guy wire, to the nearest foot.

The coordinates of midpoint P are P(-1/2, 3/2) and coordinates of midpoint Q are Q(-3/2, -4).

To find the coordinates of the midpoints P and Q of sides AB and AC, we can use the midpoint formula.

The midpoint formula states that the coordinates of the midpoint of a line segment between two points (x1, y1) and (x2, y2) are given by:

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

Using this formula, we can find the coordinates of P and Q as follows:

Coordinates of midpoint P:

P = ((2 + (-3)) / 2, (-1 + 4) / 2)

= (-1/2, 3/2)

Therefore, the coordinates of midpoint P are P(-1/2, 3/2).

Coordinates of midpoint Q:

Q = ((2 + (-5)) / 2, (-1 + (-7)) / 2)

= (-3/2, -4)

Therefore, the coordinates of midpoint Q are Q(-3/2, -4).

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Let the points A(2,-1), B(-3,4), and C(-5,-7) be the vertices of triangle A B C. Let P and Q be the midpoints of the sides AB and AC respectively. Find the coordinates of P and Q. (2 marks)

Answer:

±3/5

Step-by-step explanation:

±sqrt(9/25)

We can separate this into

± sqrt(9) / sqrt(25)

Since these are perfect squares

±3/5

Answer:

a. 0.2

b. 0.42

c. 0.7

d. the solution is in the explanation

e. x and y are not independent

Step-by-step explanation:

a. from the joint probability mass function table,

p(x=1) and p(Y= 1)

= p(1,1) = 0.2

b. prob(0,0)+prob(0,1)+prob(1,0)+prob(1,1)

= 0.10 + 0.04 + 0.08 + 0.20

= 0.42

P(X ≤ 1 and Y ≤ 1) = 0.42

c. prob {X ≠ 0 and Y ≠ 0}

= prob(1,1) + prob(1,2) + prob(2,1) + prob(2,2)

= 0.20 + 0.06 + 0.14 + 0.30

= 0.7

d. we have to calculate the marginal pmf of x and y here.

we have the x values as 0,1,2

prob(x=0) = 0.1 + 0.04 + 0.02

= 0.16

prob(x=1) = 0.08 + 0.2 + 0.06

= 0.34

prob(x=2) = 0.06+0.14+0.3

= 0.50

we have y values as 0,1,2

prob(y=0) = .1+.08+.06

= 0.24

prob(y=1) = .04+.2+.14

= 0.38

prob(y = 2) = 0.02+0.06+0.3

= 0.38

P(X ≤ 1) = prob(x=0)+prob(x=1)

= 0.34+0.16

= 0.50

e. from the joint table we have this,

prob(1,1) = 0.2

prob(x=1) = 0.34

prob(y=1) = 0.38

then prob(x=1)*prob(y=1)

= 0.34*0.38

= 0.1292

therefore prob(1,1) is not equal to prob(x=1)*prob(y=1)

0.2≠0.1292

x and y are not independent

Answer:

p=20°

Step-by-step explanation:

(7p+7)°+33°=180°

7p°+7°+33°=180°

Step 1: Simplify both sides of the equation.

7p°+7°+33°=180°

(7p)°+(7+33)°=180°(Combine Like Terms)

7p°+40°=180°

7p°+40°=180°

Step 2: Subtract 40 from both sides.

7p°+40°−40°=180°−40°

7p°=140°

Step 3: Divide both sides by 7.

7p°/7°=140°/7°

p=20°

Answer:

70

Step-by-step explanation:

700 / 10 = 70

Answer:

70

Step-by-step explanation:

700 ÷ 10 = 70

We cannot conclude that there are more than 70,000 defined words in the dictionary.

To test the claim that there are more than 70,000 defined words in the dictionary, we can set up the null and alternative hypotheses as follows:

Null Hypothesis (H0): The mean number of defined words on a page is 48.0 or less.

Alternative Hypothesis (H1): The mean number of defined words on a page is greater than 48.0.

So, sample mean

= (59 + 37 + 56 + 67 + 43 + 49 + 46 + 37 + 41 + 85) / 10

= 510 / 10

= 51.0

and, the sample standard deviation (s)

= √[((59 - 51)² + (37 - 51)² + ... + (85 - 51)²) / (10 - 1)]

≈ 16.23

Next, we calculate the test statistic using the formula:

test statistic = (x - μ) / (s / √n)

In this case, μ = 48.0, s ≈ 16.23, and n = 10.

test statistic = (51.0 - 48.0) / (16.23 / √10) ≈ 1.34

With a significance level of 0.05 and 9 degrees of freedom (n - 1 = 10 - 1 = 9), the critical value is 1.833.

Since the test statistic (1.34) is not greater than the critical value (1.833), we do not have enough evidence to reject the null hypothesis.

Therefore, based on the given data, we cannot conclude that there are more than 70,000 defined words in the dictionary.

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The response will be -10 if the stated statement is accurate.

This same square root and cubed root are the two radicals we see most frequently. Since the square root is so often employed, it is customary to presume that any radical written without the need for an index is a square root. The figure above constitutes a radical taken as a whole.

An phrase that has a root, often a square or cube root, is referred to as a radical. A radical is made up of three main parts, namely: It expresses the degree of radicand multiplication. If the root symbol's numeric component is absent, it is assumed as 2 (square root). The symbol √ means “root of”.

= 6 - 4²

= 6 - 16

= - 10

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The correct questions are-

6 - 4²

Answer:

p > α

0.7038 > 0.05

Also since F < F critical

0.475 < 3.238

We failed to reject H₀

We do not have significant evidence at the given significance level to show that there is a difference among the four chemical agents on the strength of a particular type of  cloth.

Step-by-step explanation:

We are given that a chemist wishes to test the effect of four chemical agents on the strength of a particular type of  cloth.

Since we are given data for four independent chemical agents to determine the effect on the strength of a particular type of cloth, therefore, a one-way analysis of variance may be used for the given problem.

ANOVA:

The one-way analysis of variance (ANOVA) may be used to find out whether there is any significant difference between the means of two or more independent categories of data.

Set up hypotheses:

Null hypotheses = H₀: μ₁ = μ₂ = μ₃ = μ₄

Alternate hypotheses = H₁: μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄

Set up decision rule:

We Reject H₀ if p ≤ α

OR

We Reject H₀ if F > F critical

ANOVA in Excel:

Step 1:

In the data tab, select data analysis

Step 2:

Select "Anova single factor" from the analysis tools

Step 3:

Select the destination of input data in the "input range"

Step 4:

Select "rows" for the option "Group By"

Step 5:

Tick the option "labels in first row"

Step 6:

Set alpha = 0.05

Step 7:

Select the destination of output data in the "output options"

Conclusion:

Please refer to the attached results.

The p-value is found to be

p = 0.7038

The F value is found to be

F = 0.475

The F critical value is found to be

F critical = 3.238

Since p > α

0.7038 > 0.05

We failed to reject H₀

Also since F < F critical

0.475 < 3.238

We failed to reject H₀

We do not have significant evidence at the given significance level to show that there is a difference among the four chemical agents on the strength of a particular type of cloth.

Answer:

x> 5/4

Step-by-step explanation:

9<4(x+9)−7−25

Step 1: Simplify both sides of the inequality.

9<4x+4

Step 2: Flip the equation.

4x+4>9

Step 3: Subtract 4 from both sides.

4x+4−4>9−4

4x>5

Step 4: Divide both sides by 4.

4x/4>5/4

x>5/4

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Answer:

Step-by-step explanation:

18 * 10 - 8 * 4    (remember pemdas)

180 - 32 =

148 cm²

The implications of Constructivist approach in teaching mathematics is that it helps the students to develop a better way to comprehend the content of what they are being taught.

A constructive approach of teaching mathematics believes that students construct knowledge rather than just passively take in information.

A constructive approach of teaching also believes that students integrate new knowledge with existing knowledge to create a deeper understanding of the mathematics being taught to them.

Therefore, constructive approach of teaching can help the students to comprehend the content of what they are being taught.

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Answers:

5)

a.Highest- 96

Lowest-52

b.74

c. 70-80

d. 13

e. 7

6)

a. 89%

b. 51%

c. In the morning(89%)

The value of t₄ in the arithmetic sequence is 103/8.To determine the value of t₄ in an arithmetic sequence, we need to use the given information that t₁ = 11 (the first term of the sequence) and S₉ = 243 (the sum of the first 9 terms of the sequence).

We know that the formula for the sum of an arithmetic sequence is Sₙ = (n/2)(2a + (n-1)d), where Sₙ is the sum, a is the first term, n is the number of terms, and d is the common difference.

From the given information, we have S₉ = 243, a = 11, and n = 9. Plugging these values into the sum formula, we can solve for d:

243 = (9/2)(2(11) + (9-1)d)

243 = 9(22 + 8d)

243 = 198 + 72d

45 = 72d

d = 45/72 = 5/8

Now that we have the common difference, we can find t₄ using the formula for the nth term of an arithmetic sequence:

tₙ = a + (n-1)d

t₄ = 11 + (4-1)(5/8)

t₄ = 11 + 3(5/8)

t₄ = 11 + 15/8

t₄ = 88/8 + 15/8

t₄ = 103/8

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(i) \(\lim_{x \to \pi/3}\) f(x) = 1 + √3.

(ii) \(\lim_{x \to \frac{\pi}{4}} f(x)\) does not exist.

For λ = 2.5, the function f(x) will be continuous at x = 0.

Given the function is,

f(x) = 1.5, when x = 0

    = 1 -2 sin x, when x < π/4

    = 1 + 2 sin x, when x > π/4

    = 1 + (sin λx/sin 5x)

Now,

\(\lim_{x \to \pi/3}\) f(x) = \(\lim_{x \to \pi/3}\) (1 + 2 sin x) [Since, π/3 > π/4]

                    = 1 + 2 sin (π/3)

                    = 1 + 2√3/2 = 1 + √3

Hence, \(\lim_{x \to \pi/3}\) f(x) = 1 + √3.

Now left hand limit is,

\(\lim_{x \to \frac{\pi^+}{4}}\) f(x) = \(\lim_{x \to \frac{\pi^+}{4}}\) (1 + 2sin x) = 1 +2 sin(π/4) = 1 + 2*(1/√2) = 1 + √2

and right hand limit is,

\(\lim_{x \to \frac{\pi^-}{4}}\) f(x) = \(\lim_{x \to \frac{\pi^-}{4}}\) (1 - 2 sin x) = 1 - 2*(1/√2) = 1 - √2

Since left hand limit and right hand limit are not equal so value of \(\lim_{x \to \frac{\pi}{4}} f(x)\) does not exist.

\(\lim_{x \to 0}\) f(x) = \(\lim_{x \to 0}\) (1 + (sin λx/sin 5x)) = 1 + \(\lim_{x \to 0}\) ((sin λx/λx)/(sin 5x/5x))*(λ/5) = 1 + λ/5

Since f(x) is continuous at x = 0.

So, \(\lim_{x \to 0}\) f(x) = f(0)

1 + λ/5 = 1.5

λ/5 = 1.5 - 1 = 0.5

λ = 2.5

Hence the value of λ will be 2.5.

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A statistical question that can result in numerical data is How many times did you go swimming this year? So, the correct option is A).

The statistical question that can result in numerical data is "How many hours this week did you spend on homework?" and "How many times did you go swimming this year?".

These questions involve counting or measuring quantities, which can be represented using numerical data. The other two questions do not involve numerical data and therefore cannot be considered statistical questions that result in numerical data. So, the correct answer is B).

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Answer:

How many pink erasers do the students in your class have?