What is the following difference?
11 45-45
7 √40
14 √10
29 √5
95 √5

Answer:

A positive number.

Any negative subtracted from a positive will always be positive.

Answer:

a-b will be and will always be a POSITIVE number.

This is because a is positive, and b is negative.

However, when you subtract a negative number, you are actually just adding it.

So, a - (-b) = a+b.

This is why, it will always be positive.

Let me know if this helps!

Answer:

-3

Step-by-step explanation:

See attached image

the rate of change of the radius at the instant the volume equals 36π cm³ is 7 / (36π) cm/sec.

The volume V of a sphere with radius r is given by the formula V = (4/3)πr³. We are given that the rate of change of the volume is 7 cm³/sec. Differentiating the volume formula with respect to time, we get dV/dt =(4/3)π(3r²)(dr/dt), where dr/dt represents the rate of change of the radius with respect to time.

We are looking for the rate of change of the radius, dr/dt, when the volume equals 36π cm³. Substituting the values into the equation, we have: 7 = (4/3)π(3r²)(dr/dt)

7 = 4πr²(dr/dt) To find dr/dt, we rearrange the equation: (dr/dt) = 7 / (4πr²) Now, we can substitute the volume V = 36π cm³ and solve for the radius r: 36π = (4/3)πr³

36 = (4/3)r³

27 = r³

r = 3  Substituting r = 3 into the equation for dr/dt, we get: (dr/dt) = 7 / (4π(3)²)

(dr/dt) = 7 / (4π(9))

(dr/dt) = 7 / (36π)

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The length ST of the triangle STU is 12.2 units.

Similar triangles are the triangles that have corresponding sides in

proportion to each other and corresponding angles equal to each other.

Therefore, using the similarity ratios, the side ST of the triangle STU can be found as follows:

Therefore,

PQ / ST = QR / TU

Hence,

61 / ST = 50 / 10

cross multiply

610 = 50 ST

divide both sides by 50

ST = 610 / 50

ST = 610 / 50

ST = 12.2 units

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a. There is sufficient evidence to conclude that there is a significant difference in the mean maximum output of moisture between the two brands of ultrasonic humidifiers.

b. We are 95% confident that the true difference in mean maximum output of moisture between the two brands of ultrasonic humidifiers lies between 0.394 oz and 3.006 oz.

To test if there is a difference in the mean maximum output of moisture between the two brands of ultrasonic humidifiers, we can set up the following hypotheses:

Null Hypothesis (H₀): The mean maximum output of moisture for both brands is equal.

Alternative Hypothesis (H₁): The mean maximum output of moisture for the two brands is different.

To perform the test, we will use the pooled procedure assuming equal variances. Let's calculate the necessary statistics and perform the hypothesis test.

(a) Hypothesis Testing:

Let's denote:

n₁ = sample size of Brand 1 = 4

n₂ = sample size of Brand 2 = 4

x₁ = sample mean of Brand 1 = (14.0 + 14.3 + 12.2 + 15.1) / 4 = 55.6 / 4 = 13.9 oz

x₂ = sample mean of Brand 2 = (12.1 + 13.6 + 11.9 + 11.2) / 4 = 48.8 / 4 = 12.2 oz

s₁ = sample standard deviation of Brand 1

s₂ = sample standard deviation of Brand 2

To calculate the pooled standard deviation (spooled), we use the following formula:

spooled = sqrt(((n₁ - 1) * s₁² + (n₂ - 1) * s₂²) / (n₁ + n₂ - 2))

Now, we can calculate the test statistic (t-value) using the formula:

t = (x₁ - x₂) / (spooled * sqrt(1/n₁ + 1/n₂))

Since we assume equal variances, we can combine the variances and degrees of freedom using the formula:

df = n₁ + n₂ - 2

We will compare the calculated t-value to the critical value from the t-distribution with (df) degrees of freedom to determine the result of the hypothesis test.

(b) Confidence Interval:

To construct a 95% confidence interval, we can use the formula:

CI = (x₁ - x₂) ± tα/2 * (spooled * sqrt(1/n₁ + 1/n₂))

where tα/2 is the critical value from the t-distribution corresponding to a significance level of α = 0.05 (two-tailed test) and (df) degrees of freedom.

Let's calculate the required values to perform the test and construct the confidence interval:

s₁ = sqrt((Σ(x - x')²) / (n₁ - 1))

= sqrt((14.0 - 13.9)² + (14.3 - 13.9)² + (12.2 - 13.9)² + (15.1 - 13.9)²) / (4 - 1)

≈ sqrt(0.01 + 0.16 + 1.69 + 1.21) / 3

≈ sqrt(4.07) / 3

≈ 1.07

s₂ = sqrt((Σ(x -x')²) / (n₂ - 1))

= sqrt((12.1 - 12.2)² + (13.6 - 12.2)² + (11.9 - 12.2)² + (11.2 - 12.2)²) / (4 - 1)

≈ sqrt(0.01 + 1.44 + 0.09 + 1) / 3

≈ sqrt(2.54) / 3

≈ 0.59

spooled = sqrt(((n₁ - 1) * s₁² + (n₂ - 1) * s₂²) / (n₁ + n₂ - 2))

= sqrt(((4 - 1) * 1.07² + (4 - 1) * 0.59²) / (4 + 4 - 2))

≈ sqrt((3 * 1.1449 + 3 * 0.3481) / 6)

≈ sqrt(3.4347 / 6)

≈ sqrt(0.5724)

≈ 0.757

t = (x₁ - x₂) / (spooled * sqrt(1/n₁ + 1/n₂))

= (13.9 - 12.2) / (0.757 * sqrt(1/4 + 1/4))

≈ 1.7 / (0.757 * sqrt(0.5))

≈ 1.7 / (0.757 * 0.707)

≈ 1.7 / 0.536

≈ 3.171

df = n₁ + n₂ - 2 = 4 + 4 - 2 = 6

Using a t-table or calculator, the critical value for a two-tailed test with α = 0.05 and df = 6 is approximately 2.447.

Since the calculated t-value (3.171) is greater than the critical value (2.447), we reject the null hypothesis.

Interpretation:

Based on the test results, there is sufficient evidence to conclude that there is a significant difference in the mean maximum output of moisture between the two brands of ultrasonic humidifiers.

Now, let's proceed to construct the confidence interval:

CI = (x₁ - x₂) ± tα/2 * (spooled * sqrt(1/n₁ + 1/n₂))

= (13.9 - 12.2) ± 2.447 * (0.757 * sqrt(1/4 + 1/4))

≈ 1.7 ± 2.447 * (0.757 * 0.707)

≈ 1.7 ± 2.447 * 0.534

≈ 1.7 ± 1.306

The 95% confidence interval is approximately (0.394, 3.006).

Interpretation:

We are 95% confident that the true difference in mean maximum output of moisture between the two brands of ultrasonic humidifiers lies between 0.394 oz and 3.006 oz.

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Compound amount = $8867.39

compound interest = $1867.39

EXPLANATION

Given:

Principal(p) = $7000 Rate(r) = 0.12 Time(t) = 2 n= 4

We can calculate the compound amount(A) using the formula below:

Substitute the values and evaluate.

Hence, the compound amount = $8867.39

We proceed to find the compound interest.

A = P + I

⇒ I = A - P

= 8867.39 - 7000

=1867. 39

Therefore, the compound interest = $1867.39

Answer:

B

Step-by-step explanation:

√256=16

√289=17

Answer:

b.√256 and √289 . play basketball

Answer:

cant answer without a function graphed

Step-by-step explanation:so yeah

Answer:

-9 ≤n ≤1

Step-by-step explanation:

-3 ≤ n+6 ≤ 7

Subtract 6 from all sides

-3  -6≤ n+6-6 ≤ 7-6

-9 ≤n ≤1

Alexandra's mixture has a higher percentage of black paint, making it darker than Noah's mixture.

To determine whose gray paint will be darker, we can use the percentage of black paint in each mixture.

Alexandra's mixture contains 2 cups of black paint and 1 cup of white paint. This means that the percentage of black paint in her mixture is 2/(2+1) = 2/3, or about 66.67%.

Noah's mixture contains 3 cups of black paint and 2 cups of white paint. This means that the percentage of black paint in his mixture is 3/(3+2) = 3/5, or about 60%.

Based on these percentages, we can see that Alexandra's mixture has a higher percentage of black paint, making it darker than Noah's mixture. Therefore, Alexandra's gray paint will be darker than Noah's gray paint.

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Answer:

0.4141 rounded to the nearest thousandth is 0.414.

Step-by-step explanation:

Since the number is 0.4141, and the number following the thousandths place is under 5, the thousandth place stays the same. If it were 5 or over, it would round up making it 0.415, but it's not so it is 0.414.

Answer:

−(6x−12)−(−20)−7x

Distribute:

=−6x+12+20+−7x

Combine Like Terms:

=−6x+12+20+−7x

=(−6x+−7x)+(12+20)

=−13x+32

Answer:

=−13x+32

Answer:

\(y - 3 = - 4(x + 2)\)

Answer:

a) 6 units

b) 6 units

c) 10 units

d) 15 units

Answer: a = 6

b = 6

c = 10

d = 15

Step-by-step explanation: Use the distance formula √(x2 - x1)^2 + (y2 - y1)^2

Answer:

5. Obtuse

6. Right

7. Acute

Step-by-step explanation:

5. 5,12,15

The square of the longest side is 15^2 = 225. The sum of the squares of the two shorter sides is 5^2 + 12^2 = 169. Since 169 < 225, the triangle is obtuse.

6. 6,8,10

The square of the longest side is 10^2 = 100. The sum of the squares of the two shorter sides is 6^2 + 8^2 = 100. Since 100 = 100, the triangle is right.

7. 12,10,13

The square of the longest side is 13^2 = 169. The sum of the squares of the two shorter sides is 12^2 + 10^2 = 244. Since 244 > 169, the triangle is acute.

Answer:

A

Step-by-step explanation:

if you want the step by step, let me know (:

Answer:

a

Step-by-step explanation:

Answer: vertex: (1/2,11/4)

a of s: x=1/2

y-intercept: (0,3)

Step-by-step explanation:

Answer:

15.9%.

Explanation:

The mean = 39.5

Standard deviation = 18

Raw Value, X=21.5

To find the probability that a person chosen at random from this church is ages 21.5 or younger, we first find the Z-Score.

Next, we check the P-Value from the Z-Table.

Therefore, the probability that a person chosen at random from this church is ages 21.5 or younger is 15.9%.

Step-by-step explanation:

what do we need to do ?

just solve the system of 2 equations ?

as we have x and -x in the equations, we simply add both equations, get one summary equation just in y, solve for y, and then use one of the original equations to solve for x :

y = x - 4

y = -x + 2

----------------

2y = 0 - 2

2y = -2

y = -1

-1 = x - 4

3 = x

x = 3

y = -1

Answer:

Question (a)

Given equation:

\(8^{2x} = 32^{x+3}\)

8 can be written as \(2^3\)

32 can be written as \(2^5\)

Therefore, we can rewrite the equation with base 2:

\(\implies (2^3)^{2x} = (2^5)^{x+3}\)

------------------------------------------------------------------------------

Question (b)

To solve:

\((2^3)^{2x} = (2^5)^{x+3}\)

Apply the exponent rule \((a^b)^c=a^{bc}\) :

\(\implies 2^{3 \cdot 2x} = 2^{5(x+3)}\)

\(\implies 2^{6x} = 2^{5x+15}\)

\(\textsf{If }a^{f(x)}=a^{g(x)}, \textsf{ then } f(x)=g(x)\) :

\(\implies 6x = 5x+15\)

Subtract \(5x\) from both sides:

\(\implies x = 15\)

The answer as a decimal to the nearest hundredth is -3.45.

For the given question;

The expression is given as;

= -3.7 + 1/4

Now, the fraction 1/4 can be written in decimal as 0.25.

Put the value of 1/4.

=  -3.7 + 0.25

The subtraction of larger negative to smaller positive gives negative number.

= -3.45

Thus, the answer as a decimal to the nearest hundredth is -3.45.

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Answer:

Step-by-step explanation:

Errrr....this is kind of big brain for me. also i'm new here. hope somebody else can answer you.

Answer:

the sales tax is 10%

Step-by-step explanation:

710 plus 10% is 781

Answer:

The Median is 75

Step-by-step explanation:

median is the middle number in a set of given numbers

arranging in order will be

30,64,70,80,90,110

the middle numbers are 70 and 80

Median=80+70/2

=150/2

Median=75

Answer:

21

Step-by-step explanation:

First determine the amount of tax

20 * .05

1

Add this to the original amount

20+1

21

He will pay 21 dollars