Spencer and Hanna buy a pizza for $18 that is half pepperoni and half veggie. They cut the pizza into 8 slices.

Georgia works part-time at a daycare while she is going to college. She earned $160 last week. Georgia worked 12 more hours than

Lelu [443]

Answer:

B. $8

Step-by-step explanation:

Given:

Total payment, T = $160

Hourly rates = $t/hour

= total payment/total time worked

The question said, "worked 12 more hours than the amount she is paid per hour".

Total time worked = (12 + t) hour

Therefore, Hourly rates of payment, t = 160/(12 + t)

t^2 + 12t - 160 = 0

Solving the above quadratic equation,

t = -20 and 8

t = $8

3 0

3 years ago

Will mark brainliest and 10 points

KengaRu [80]

Answer:

Student 3

Step-by-step explanation:

Part of the 3-4-5 Pythagorean triples.

8 0

3 years ago

A metropolitan transportation authority has set a bus mechanical reliability goal of 3,800 bus miles. Bus mechanical reliability

DaniilM [7]

Answer:

(A) T-stat = 1.82

(B) Critical value is 1.645

(C) Yes, there is sufficient evidence to reject the null hypothesis using a 0.05 significance level.

Step-by-step explanation:

(A) T-stat (z) = (sample mean - population mean) ÷ sd/√n

sample mean = 3850 bus miles

population mean = 3800 bus miles

sd = 275 bus miles

n = 100

z = (3850 - 3800) ÷ 275/√100 = 50 ÷ 275/10 = 50 ÷ 27.5 = 1.82

(B) The test is a one-tailed test. The critical value is obtained from the standard normal distribution table. The critical value using a 0.05 significance level is 1.645

(C) Null hypothesis: The bus mechanical reliability is 3850 bus miles.

Alternate hypothesis: The bus mechanical reliability is less than 3850 bus miles.

Conclusion:

There is sufficient evidence to reject the null hypothesis because the test statistic (1.82) is greater than the critical value (1.645)

6 0

3 years ago

What is the reason for each step in the solution of the inequality? 4(x+6)>−5(x+5)−14 Select the reason for each step from th

Nesterboy [21]

Hey there!!

The equation given :

4 ( x + 6 ) > -5 ( x + 5 ) - 14

... 4x + 24 > -5x - 25 - 14

... 4x + 24 > - 5x - 39

Add 39 on both sides

... 4x + 63 > - 5x

Subtract 4x on both sides

... 63 > - 9x

Divide by -9 on both sides

When we divide both sides by a negative number, we switch the signs.

... -7 < x

Hope my answer helps!!

8 0

3 years ago

Read 2 more answers

Please help if you know how to integrate using substitution.

mrs_skeptik [129]

Answer:

B. $\displaystyle \frac{-1}{2}ln|cos2x| + C$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Calculus

Antiderivatives - Integrals

Integral Constant C

U-Substitution

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Trig Integration: $\displaystyle \int {tan(u)} \, du = -ln|cosu| + C$

Step-by-step explanation:

Step 1: Define

$\displaystyle \int {tan(2x)} \, dx$

Step 2: Identify Variables

Set variables for u-substitution.

u = 2x

du = 2dx

Step 3: Integrate

[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \frac{1}{2}\int {2tan(2x)} \, dx$
[Integral] U-Substitution: $\displaystyle \frac{1}{2}\int {tanu} \, du$
[Integral] Trig Integration: $\displaystyle \frac{1}{2}(-ln|cosu|) + C$
[Integral] Back-Substitute: $\displaystyle \frac{-1}{2}ln|cos2x| + C$

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Integration

Book: College Calculus 10e

7 0

3 years ago