a tree casts a 9 ft shadow at the same time that a person 6 ft tall casts a 4 ft shawdow. what is the height of the tree?

Answer:

[tex]\frac{3}{2}[/tex]

Step-by-step explanation:

Here, the given expression is,

[tex]5(4x-10)+10x=4(2x-3)+2(x-4)[/tex]

By distributive property,

[tex]20x - 50 + 10x = 8x - 12 + 2x - 8[/tex]

By combining like terms,

[tex]30x -50=10x-20[/tex]

Adding 50 on both sides,

[tex]30x=10x-20+50[/tex]

[tex]30x = 10x + 30[/tex]

Subtracting 10x on both sides,

[tex]20x = 30[/tex]

Divide both sides by 20,.

[tex]x=\frac{3}{2}[/tex]

Hence, LAST option is correct.

Angle BAC is congruent to angle DCA by the alternate interior angles theorem. Option B is correct.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

here,
The pro[perty of parallel lines states that when two parallel lines intersect by the same transversal line the alternate interior angle will be equal as also the alternate exterior angles.

So,
Line BC and AB are parallel lines and AC is a transversal line,
So,

Angle BAC  = angle DCA

Thus, angle BAC is congruent to angle DCA by the alternate interior angles theorem. Option B is correct.

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The correct number of different meal combinations that customers can make from the menu items at the Greasy Grab Bag is 24.

To determine the number of different meal combinations, we need to consider that each meal consists of one sandwich, one side, and one drink. Given that there are 4 sandwiches, 3 sides, and 2 drinks to choose from, we can calculate the total number of combinations by multiplying the number of choices for each category together.

The number of sandwich choices is 4, the number of side choices is 3, and the number of drink choices is 2. Therefore, the total number of meal combinations is calculated as follows:

Total combinations = Number of sandwich choices — Number of side choices — Number of drink choices

Total combinations = [tex]$4 \times 3 \times 2$[/tex]

Now, let's calculate the total number of combinations:

Total combinations =[tex]$4 \times 3 \times 2 = 12 \times 2 = 24$[/tex]

Thus, there are 24 different meal combinations that customers can make, which means the Greasy Grab Bag's claim of 20 different meal combinations is incorrect. The correct number is 24.

Final answer:

The value of I for the given values of W and R can be calculated using the formula I = [tex]\sqrt{(W/R)[/tex]. For W = 100 and R = 25, the value of I is 2 amperes. For W = 100 and R = 50, the value of I is approximately 1.41 amperes.

Explanation:

The formula I = [tex]\sqrt{(W/R)[/tex]  gives the electric current in amperes that flows through an appliance, where W is the power in watts and R is the resistance in ohms.

To determine the value of I for the given values of W and R, we can simply substitute the values into the formula. For the first set of numbers, W = 100 and R = 25:

[tex]I = \sqrt{(100/25)} = \sqrt{(4)} = 2[/tex] amperes.

For the second set of numbers, W = 100 and R = 50:

[tex]I = \sqrt{(100/50)} = \sqrt{(2) }[/tex]≈ 1.41 amperes.

Therefore, the value of I for the first set of numbers (W = 100, R = 25) is 2 amperes, and the value of I for the second set of numbers (W = 100, R = 50) is approximately 1.41 amperes.

P(X≤−1.9)=0.0287165598160018P(X≤−1.9)=0.0287165598160018

P(X≥1.7)=0.044565462758543P(X≥1.7)=0.044565462758543

P(−1.95996398454005≤X≤1.95996398454005)=0.95

Answer:

92.67% probability of obtaining a z value between -1.9 to 1.7.

Step-by-step explanation:

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

For a standard normal distribution, the probability of obtaining a z value between -1.9 to 1.7 is

This probability is the pvalue of z = 1.7 subtracted by the pvalue of z = -1.9.

z = 1.7 has a pvalue of 0.9554.

z = -1.9 has a pvalue of 0.0287.

So there is a 0.9554-0.0287 = 0.9267 = 92.67% probability of obtaining a z value between -1.9 to 1.7.

Linear regression describes the extent to which an independent variable predicts a dependent variable through a linear relationship.

Linear regression describes the extent to which an independent variable (x) predicts a dependent variable (y) through a linear relationship.

For example, if we have data that shows the number of hours studied (x) and the test score (y) of students, linear regression can help us determine how well the number of hours studied predicts the test score.

The regression line is used to model the linear relationship between the independent and dependent variables in the population.

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Answer:

$30838.80

:3 simply it pls

a circle has 360 degrees

 the ferris wheel has 32 cars so the circle is broken up into 32 sections

 the central angle would be the angle between 2 of the cars

 so divide 360 by 32

360/32 = 11.25 degrees

The proportion is solved and the cost of 18 bumper stickers is $ 12.96.

Given data:

To find out how much 18 bumper stickers cost, use a proportion since the cost of bumper stickers is directly proportional to the number of stickers.

Cost of 12 bumper stickers / Number of 12 bumper stickers = Cost of 18 bumper stickers / Number of 18 bumper stickers

On simplifying the proportion:

$8.64 / 12 = x / 18

Now, solve for x (the cost of 18 bumper stickers):

x = ($8.64 / 12) * 18

x = $12.96

Hence, 18 bumper stickers cost $12.96.

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0.8x – 12

The sale price is (x-15). After the 20% discount, the final price is 0.80 times the sale price, so is ...

... final price = 0.80×(x -15) = 0.80x -12

Answer:

The correct option is B.

Step-by-step explanation:

Let the original price of the jacket be x.

A jacket is on sale for $15 off. As part of a one-day sale, a 20% discount is applied to all purchases.

The price of jacket after $15 off is [tex]x-15[/tex].

Then 20% discount is applied, so the final price of the jacket is

[tex]P=(x-15)(1-\frac{20}{100})[/tex]

[tex]P=(x-15)(1-0.2)[/tex]

[tex]P=(x-15)(0.8)[/tex]

[tex]P=0.8x-12[/tex]

The final price of the jacket during this sale is 0.8x-12. Therefore the correct option is B.

Final answer:

The probability that the first item selected is good and the second item is defective is 22/105.

Explanation:

To find the probability that the first item selected is good and the second item is defective, we need to consider the total number of items, the number of good items, and the number of defective items.

The total number of items is 15, with 11 being good and 4 being defective. When we select the first item, there are 15 options, out of which 11 are good. Therefore, the probability of selecting a good item first is 11/15.

After selecting the first item, there are now 14 items left in the box, with 10 being good and 4 being defective. When we select the second item, there are 14 options, out of which 4 are defective. Therefore, the probability of selecting a defective item second is 4/14, which simplifies to 2/7.

To find the probability that both events occur, we multiply the probabilities: (11/15) * (2/7) = 22/105.

Final answer:

To estimate the product of 7 and 7956, round 7956 to 8000 and then multiply by 7 to get 56,000. The exact product, calculated using the multiplication algorithm, is 55,692.

Explanation:

To estimate the product of 7×7956, we can round 7956 to the nearest thousand which gives us 8000. Then, we multiply 7×8000 to get an estimated product of 56,000. To find the exact product, we multiply 7 by 7956 to get 55,692.

When calculating such a product, we use the multiplication algorithm where we multiply each digit of the second number by the first number and then add up the resulting values.

Here's how you would perform the multiplication step by step:

7×7 = 49, add the carried over 6 to get 55, write down 5 and carry over the 5.

After placing the digits in their correct positions, we get the final answer: 55,692. Therefore, the exact product of 7×7956 is 55,692.