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mariarad [96]
2 years ago
6

Katherine is working two summer jobs, making $16 per hour lifeguarding and making $6 per hour walking dogs. In a given week, she

can work a maximum of 15 total hours and must earn at least $160. If Katherine worked 2 hours walking dogs, determine the minimum number of whole hours lifeguarding that she must work to meet her requirements. If there are no possible solutions, submit an empty answer.
Mathematics
1 answer:
kipiarov [429]2 years ago
7 0

Answer:

Katherine need to work minimum 10 hours lifeguarding to meet her requirements

Step-by-step explanation:

Given:

Rate for Lifeguarding = $16\ per\ hour

Rate for walking dogs = $6 \ per\ hour

She had worked 2 hours walking dog

Money for walking dogs = Rate for walking dogs\times hours worked=\$6\times2=\$12

she can work a maximum of 15 total hours and must earn at least $160.

Let hours required for lifeguarding be x

Money for life guarding = Rate for walking dogs\times hours worked for lifrguarding= \$16 \timesx=16x

Total Money she must earn = Money for lifeguarding + Money for walking dogs

16x+12=160\\16x=160-12\\16x=148\\x=\frac{148}{16}=9.25 \ hours

Rounding to nearest hour

Katherine need to work minimum 10 hours lifeguarding to meet her requirements

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Find how many quarts of 6?% butterfat milk and 3?% butterfat milk should be mixed to yield 30 quarts of 5?% butterfat milk
Mrrafil [7]

Answer:

The 20  quarts are used for 6% butterfat milk and 10 quarts are used for  3% butterfat milk .

Step-by-step explanation:

As given

6% butterfat milk and 3% butterfat milk should be mixed to yield 30 quarts of 5% butterfat milk .

Let us assume that x quarts are used for 6% butterfat milk .

Than (30 - x) quarts are used for 3% butterfat milk .

6% is written in the decimal form

= \frac{6}{100}

= 0.06

3% is written in the decimal form

= \frac{3}{100}

= 0.03

5% is written in the decimal form

= \frac{5}{100}

= 0.05

Than the equation becomes

0.06 × x + (30 - x) × 0.03 = 30 × 0.05

0.06x + 0.9 - 0.03x = 1.5

0.06x  - 0.03x = 1.5 - 0.9

0.03x  = 0.6

x = \frac{0.6}{0.03}

x = 20 quarts for 6% butterfat milk  .

(30 - x ) = (30 - 20) = 10 quarts for 3% butterfat milk  .

Than 20  quarts are used for 6% butterfat milk and 10 quarts are used for  3% butterfat milk .




5 0
3 years ago
Write an equation for line L in​ point-slope form and​ slope-intercept form.
Natalka [10]
Line L's slope intercept form is

y = 4x + 7

It's point slope form is

y - 3 = 4 (x - -1)

You can check the point slope form and match it with the slope intercept form:

y - 3 = 4 (x - -1)

y - 3 = 4x + 4

y = 4x + 7

y = 4x + 7  = y = 4x + 7
4 0
3 years ago
Read 2 more answers
In Δ A B C, the measure of the largest angle is 32 less than 3 times the smallest angle. The measure of the middle angle is 8 mo
AlladinOne [14]

Answer:

52degrees

Step-by-step explanation:

Let the measure of the largest angle be x

middle angle be y

smallest angle be z

Since the sum of angle in a triangle is 180 degrees, hence;

x + y + z = 180 .... 1

If the measure of the largest angle is 32 less than 3 times the smallest angle, then;

x = 3z - 32

3z = x+ 32

z = x+32/3 ..... 2

If he measure of the middle angle is 8 more than half the measure of the largest angle, then;

y = x/2 + 8 .... 3

Substitute 2 and 3 into 1;

x + x/2 + 8 + (x+32)/3 = 180

multiply through by 6

6x + 3x + 48 + 2(x+32) = 1080

9x + 48 + 2x + 64 = 1080

11x + 112 = 1080

11x = 1080-112

11x = 968

x = 968/11

x = 88 degrees

Get the middle angle y;

Since y = x/2 + 8

y = 88/2 + 8

y = 44 + 8

y = 52 degrees

Hence the measure of the middle angle is 52degrees

5 0
3 years ago
Assume that we want to construct a confidence interval. Do one of the​ following, as​ appropriate:_________.
andreyandreev [35.5K]

Answer:

B. z Subscript alpha divided by 2 zα/2 = 1.96.

Step-by-step explanation:

We are given that we want to construct a confidence interval. For this, the summary statistics for randomly selected weights of newborn​ girls:

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As we can clearly see here that the population standard deviation is unknown and the sample size is also very large.

It has been stated that when the population standard deviation is unknown, we should use t-distribution but since the sample size is very large so we can use z distribution also as it is stated that at very large samples; the t-distribution corresponds to the z-distribution.

Here, \alpha = level of significance = 1 - 0.95 = 0.05 or 5%

         \frac{\alpha}{2}=\frac{0.05}{2} = 0.025 or 2.5%

So, the value of Z_(_\frac{\alpha}{2} _) in the z table is given as 1.96 with a 2.5% level of significance.

3 0
3 years ago
HELP image is provided
Hitman42 [59]

Answer:

yes

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angles z and b both have 2 congruent lines

angle y and a have one congruent line

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