MATHEMATICS HIGH SCHOOL

Four hundred vouchers were sold for a carwash. Vouchers to wash trucks were $4, while vouchers to wash compact cars were $3. If the total sales were $1350, how many of each type of voucher were sold?

Answers

Answer 1

Answer:

150 vouchers to wash trucks were sold

250 vouchers to wash compact cars were sold

Step-by-step explanation:

Here, we are interested in calculating the number of each type of vouchers sold.

Let the number of vouchers to wash trucks be x while the number of vouchers to wash compact trucks be y.

Firstly, we know that both sums up to be 400.

Mathematically;

x + y = 400 •••••••••(i)

Secondly,

since a voucher to wash trucks sell $4, and we sold a total of x, the amount generated from selling is 4 * x = $4x

Same way for the vouchers to wash compact cars, we have a total of $3 * y = $3y

The sum of both gives $1350, which is the total sales.

Mathematically;

4x + 3y = 1350 ••••••(ii)

So we have two equations to solve simultaneously;

x + y = 400

4x + 3y = 1350

Multiply equation i by 4 , we have;

4x + 4y = 1600

4x + 3y = 1350

Subtract equation ii from i, we have 4y-3y = 1600-1350

y = 250

From equation 1, we know that

x + y = 400

This means that;

x = 400 -y

x = 400 -250

x = 150

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In two or more complete sentences, describe why the range of y = cos(x) is -1 ≤ y ≤ 1. Make sure to reference the unit circle in your description.

Answers

Answer:

The range of cos(x) is -1 to 1 (with brackets if in interval notation as -1 and 1 can be included) is because the radius of the unit circle is also 1. If the range went past -1 or 1, the unit circle could not define those values, and would turn up as error or undefined. Now, if you replace a in y = acos(x) + b, the range would be different because you amplified the equation and thus the range and radius.

Step-by-step explanation:

a(1)= 3 5 a(n)=a(n−1)⋅(−9) What is the 3^{\text{rd}}3 rd 3, start superscript, start text, r, d, end text, end superscript term in the sequence?

Answers

Answer: -630

Step-by-step explanation:

Given the nth term of a sequence;

a(n)=a(n−1)⋅(−9) and the first term of the sequence a(1) as 35, the third term of the sequence can be gotten by using the formula at when n = 3

If n = 3 and a(1) = 35;

a(3) = 35(3-1)•(-9)

a(3) = 35×2×-9

a(3) = 70×-9

a(3) = -630

There the 3rd term of the series will give us -630 according to the nth term of the formula given.

Final answer:

The problem is about a recursive sequence where each term is the previous term multiplied by -9. After applying this rule twice, it is found that the 3rd term of the sequence is 243.

Explanation:

The problem provided indicates a recursive sequence, where each term is based on the previous term. The sequence is defined as a(1) = 3 and a(n) = a(n - 1) ⋅ (−9), which essentially means that each subsequent term is the previous term multiplied by -9.

To find the 3rd term, we apply this rule twice starting from the first term:

a(2) = a(1) * (-9) = 3 * (-9) = -27

a(3) = a(2) * (-9) = -27 * (-9) = 243

Therefore, the 3rd term of the sequence is 243.

Learn more about Recursive sequence here:

brainly.com/question/36771236

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A 50 meter path surrounds a rectangular garden . The width of the garden is two-thirds its length. find its area.

Answers

$w-width\nl-length\n\n2w+2l=50\to w+l=25\nw=(2)/(3)l\n\nsubstitute:\n\n(2)/(3)l+l=25\n\n(5)/(3)l=25\ \ \ \ /\cdot(3)/(5)\n\nl=15\ (m)\n\nw=(2)/(3)\cdot15=10\ (m)\n\nArea:A_{\fbox{ }}=wl\to A_{\fbox{ }}=10\cdot15=150\ (m^2)$

Do arthetic sequence have a common ratio?

Answers

Answer:

yes

Step-by-step explanation:

its called the common ratio because it is the same to each number or common and it also is the ratio between two consecutive numbers in the sequence

Answer:

points

Step-by-step explanation:

On discovering that her family had a 70% risk of heart attack, Erin took a treadmill test to check her own potential of having a heart attack. The doctors told her that the reliability of the stress test is 67%. The test predicted that Erin will not have a heart attack. What is the probability after the test was taken that she will have a heart attack?A. 0.4051

B. 0.5010

C. 0.4653

D. 0.6632

Answers

On discovering that her family had a 70% risk of heart attack, Erin took a treadmill test to check her own potential of having a heart attack. The doctorstold her that the reliability of the stress test is 67%. The test predicted that Erin will not have a heart attack. The probability after the test was taken that she will have a heart attack is "B. 0.501."

Answer:

The probability that she will not have a heart attack and the test predicts that she will is 0.4653 or 46.53%

Step-by-step explanation:

Hint- This a conditional probability problem where Bayes theorem should be applied.

Applying Bayes theorem,

$P(\text{No heart attack}\ |\ \text{Correctly tested})=$

$\frac{P(\text{Correctly tested}\ |\ \text{No heart attack})\cdot P(\text{No heart attack})}{P(\text{Correctly tested})}$

$P(\text{Correctly\ tested}\ |\ \text{No\ heart\ attack})=67\%=0.67$

$P(\text{No\ heart\ attack})=1-P(\text{heart\ attack})=1-0.7=0.3$

$P(\text{Correctly\ tested})=[P(\text{No\ heart\ attack})* P(\text{Correctly\ tested})]+[P(\text{Heart\ attack})* (\text{Incorrectly\ tested})]$

$=[0.3* 0.67]+[0.7* 0.33]=0.432$

Putting the values,

$P(\text{No\ heart\ attack}\ |\ \text{Correctly\ tested})=(0.67* 0.3)/(0.432) =0.4653$

∴ There is a probability of 0.4653 or 46.53% chance that she will not have a heart attack even though the test predicts that she will.

Rewrite the equation below so that it does not have fractions

2/3x-5=3/4

Answers

Answer:

Step-by-step explanation:

The best way to do this problem is to find the lowest common denominator.

2/3 : 3*2/(3*3)

3/4 : 3*3 / 3*4

Notice what you have done. You have multiplied both denominators by something that gets rid of the denominators, or will when you multiply by 4 * 3 = 12

So multiply the equation by 12

(2/3 x- 5 = 3/4 ) 12

8x - 60 = 9 Add 60 to both sides

8x - 60 = 9 Combine

8x = 69 Divide by 8

x = 69/8

x = 8 5/8

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