Use the equation below to answer the following questions.

a. If you apply the Distributive Property first to solve the equation, what operation will you need to use last?


b. If instead you divide first to solve the equation, what operation would you need to use last?


And use the equation: 6 ( d/3 - 5 ) = 34

Please answer fast i have a test and only 3 mins left

Answer:

answer is 24 hope this helps! :)

Answer:

the answer is 105

Step-by-step explanation:

because 5×3=15 so 15×7 =105

The 99% confidence interval for the true population mean backpack weight is approximately (68.15, 71.85) ounces, rounded to two decimal places.

To construct a 99% confidence interval for the true population mean backpack weight, we can use the formula:Confidence Interval = Sample Mean ± (Critical Value * Standard Deviation / √Sample Size).

Since the population standard deviation is known, we can use the z-distribution and find the critical value corresponding to a 99% confidence level. The critical value for a 99% confidence level is approximately 2.576.

Given that the sample mean weight is 70 ounces, the population standard deviation is 6.4 ounces, and the sample size is 48, we can calculate the confidence interval:

Confidence Interval = 70 ± (2.576 * 6.4 / √48).

Simplifying the expression, we get:

Confidence Interval ≈ 70 ± 1.855.

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Step-by-step explanation:

First, let's find the area of the rectangular sides using the dimensions given.

16 x 7 = 112 \(in^2\)

112 is just for one rectangle. We need to find the area for 3 rectangles.

112 x 3 = 336 \(in^2\)

Now, we need to find the area of the triangle. Using the formula let's find the area.

bh/2

7 x 8/2

56

Our answer is 56 as we find the area of two triangles and 28 x 2 equals 56.   To find the prism's total area, we have to add the areas altogether.

56 + 336 =

Answer: 392 \(in^2\)

Answer:

i think the answer is A 108

Step-by-step explanation:

Answer:

The answer is D hope this helps :)

Step-by-step explanation:

Answer:

i think its 12%

Step-by-step explanation:

Answer:

2000 dollars

Step-by-step explanation:

The equivalent expression is 5 - 3x/2. Option D

Algebraic expressions are described as expressions that are made up of variables, their coefficients, factors and constants.

these algebraic expressions are also composed of mathematical operations. These operations includes;

From the information given, we have that;

1/ 4(8 - 6x + 12)

expand the bracket, we have;

Add the like terms

1/4(20 - 6x)

now, multiply the values, we have;

20 - 6x/4

Divide by the denominator

5 - 3x/2

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The complete question:

Simply the expression:

1/ 4(8 - 6x + 12)

Answer:

Step-by-step explanation:

The correct definition of perpendicular lines is option 1: "Two lines that intersect in a way that forms right angles."

When two lines intersect to form four right angles (90-degree angles), they are said to be perpendicular to each other. The point at which the lines intersect is called the point of intersection.

Therefore, option 1 is the correct definitation of perpendicular lines.

Answer: 1. Two lines that intersect in a way that forms right angles.

Step-by-step explanation:

Hope this helped! :)

Answer:

(x+4)^2  -25

Step-by-step explanation:

x²+8x-9 in the form  (x+k)² +h.

We need to complete the square.

x^2 +8x   -9

Take the coefficient of x.

8

Divide by 2.

8/2 =4

Square it.

4^2 = 16

Add this then subtract i.

x^2 +8x+16    -16   -9

The x^2 +8x+16 becomes  (x+4) ^2  and we can simplify the remaining terms.

(x+4)^2  -25

If 7people are to answer the call, they must work at the rate of 12.85 calls per hour

A rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute.

The total calls available for an hour is 14×5 = 90 calls per hour

if 7 people are answering call , the the rate of calls per person is 90/7 = 12.85 calls per hour

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It would take 21 weeks for the population to surpass 16,000.

The insect population P in a certain area fluctuates with the seasons and is estimated by the function P = 15,000 + 2500 sin(πt/52), where t is given in weeks.

For the population to surpass 16,000, we can set up the following equation:

15,000 + 2500 sin(πt/52) = 16,000

Subtracting 15,000 from both sides, we get:

2500 sin(πt/52) = 1000

Dividing both sides by 2500, we get:

sin(πt/52) = 0.4

We know that sin(πt/52) is positive when t is between 0 and 52 and between 104 and 156 since sine is positive in the first and second quadrants. Therefore, we can write:

πt/52 = sin⁻¹(0.4)

Multiplying both sides by 52/π, we get:

t = (52/π) sin⁻¹(0.4)

Using a calculator, we can evaluate sin⁻¹(0.4) to be approximately 0.4115 radians.

t = (52/π) (0.4115)

t = 21.02

Therefore, it would take 21 weeks for the population to surpass 16,000.

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Given:

The given expression: 4m - 20

Required:

Using the GCF factor the expression.

Explanation:

We will solve as:

Answer:

Hence, first and second is true.

Answer:

0.005 `; 0.00499 ;

No, because np < 10 ;

2000

Step-by-step explanation:

Given that:

Number of samples , n = 100

Proportion, p = x / n

p = 1 / 200

= 0.005

p = μ

Standard deviation of sample proportion :

σp = sqrt((p(1 - p)) / n)

σp = sqrt((0.005(1 - 0.005)) / 200)

σp = sqrt((0.005(0.995)) / 200)

σp = sqrt(0.004975 / 200)

σp = sqrt(0.000024875)

σp = 0.0049874

σp = 0.00499

np = 100 * 0.005 = 0.5

n(1 - p) = 100(1-0.05) = 95

Smallest value of n for which sampling distribution is approximately normal

np ≥ 10

0.005n ≥ 10

To obtain the smallest value of n,

0.005n = 10

n = 10 / 0.005

n = 2000

Using the Central Limit Theorem, it i found that:

In this problem:

Item a:

\(\mu = p = 0.005\)

\(s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.005(0.995)}{100}} = 0.0071\)

The mean is of 0.005, with a standard deviation of 0.0071.

Item b:

\(np = 100(0.005) = 0.5\)

np < 10, hence not normal, and option C is correct.

Item c:

\(np = 10\)

\(0.005n = 10\)

\(n = \frac{10}{0.005}\)

\(n = 2000\)

The smallest value of n for the sampling distribution to be approximately normal is 2000.

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Answer:

Vertical asymptotes: x = -3/2

Horizontal asymptotes: y = 2

Answer:

a. y+7 1/2=x

s=5

Step-by-step explanation:

Answer:

The answer is 1/8+5/8=3/4

Step-by-step explanation:

8/21 of the lawn still needs to be mowed.

To compare fractions, we need a common denominator. The least common multiple of 7 and 3 is 21.

Miss Lianto's fraction: (2/7) x (3/3) = 6/21

Son's fraction: (1/3) x (7/7) = 7/21

To calculate how much of the lawn still needs to be mowed, we can subtract the combined fractions mowed from the total:

Combined fractions mowed: 6/21 + 7/21 = 13/21

So, Remaining fraction: 1 - 13/21 = 8/21

Therefore, 8/21 of the lawn still needs to be mowed.

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The time taken to cover a distance of 814 miles for Caynon's home will be 22 hours.

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.

Given that:-

The time will be calculated as:-

First, we will calculate the speed to cover the distance of Brother's house:-

Speed = Distance / Time

Speed = 481 / 13 = 37 miles per hour.

Now the time to cover a distance of 814 miles will be calculated as:-

Time = Distance / Speed

Time = 814 / 37

Time = 22 hours

Therefore the time taken to cover a distance of 814 miles for Caynon's home will be 22 hours.

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Given:-

To find:-

Answer:-

In the given right angled triangle, we may use the trigonometric ratios. We can see that the measure of the longest side is 5 which is hypotenuse and the measure of perpendicular needs to be find out .

We may use the ratio of sine here as , we know that in any right angled triangle,

\(\implies\sin\theta =\dfrac{p}{h} \\\)

And here , p = 5 and h = x , so on substituting the respective values, we have;

\(\implies \sin\theta = \dfrac{x}{5} \\\)

Again here angle is 45° . So , we have;

\(\implies \sin45^o =\dfrac{x}{5} \\\)

The measure of sin45° is 1/√2 . so on substituting this we have;

\(\implies \dfrac{1}{\sqrt2}=\dfrac{x}{5} \\\)

\(\implies x =\dfrac{5}{\sqrt2}\\\)

Value of √2 is approximately 1.414 . So we have;

\(\implies x =\dfrac{5}{1.414} \\\)

\(\implies \underline{\underline{\red{\quad x = 3.53\quad }}}\\\)

Hence the value of x is 3.53 .

and we are done!

Answer:

The length of side x to the nearest tenth is 3.5.

Step-by-step explanation:

From inspection of the given right triangle, we can see that the interior angles are 45°, 45° and 90°. Therefore, this triangle is a 45-45-90 triangle.

A 45-45-90 triangle is a special right triangle where the measures of its sides are in the ratio  1 : 1 : √2.  Therefore, the formula for the ratio of the sides is b: b : b√2 where:

We have been given the hypotenuse, so:

\(\implies b\sqrt{2}=5\)

Solve for b:

\(\implies \dfrac{b\sqrt{2}}{\sqrt{2}}=\dfrac{5}{\sqrt{2}}\)

\(\implies b=\dfrac{5}{\sqrt{2}}\)

The side labelled "x" is one of the sides opposite the 45° angles, so:

\(\implies x=b\)

Substitute the found value of b into the equation for x:

\(\implies x=\dfrac{5}{\sqrt{2}}\)

\(\implies x=3.5355339...\)

\(\implies x=3.5\;\sf(nearest\;tenth)\)

Therefore, the length of side x to the nearest tenth is 3.5.

Answer:

324

Step-by-step explanation:

Answer:

\( - \frac{ 1}{2} \cos(2x) + c\)

Answer:

Step-by-step explanation:

[-5/13] 3/5 +12+13 [-4/5 = - 63/65

The rate of change in the total amount charged with respect to the time spent on the service call is $40 per hour.

The mathematical concept of rate of change describes how much one quantity changes in relation to another. It is calculated as the difference between the change in the output (the dependent variable) and the change in the input (independent variable).

The rate of change, in other words, informs us of how quickly or slowly something is changing through time or in relation to another variable. When tracking the distance an automobile travels over time, for instance, the rate of change would be the car's speed, which is calculated as the distance traveled divided by the time required.

Slope, which is the ratio of the vertical change (rise) to the horizontal change (run) between two points on a graph, is a common way to depict the rate of change. The rate of change of the dependent variable with respect to the independent variable is depicted by the slope of a straight-line graph.

The rate of change in the total amount charged with respect to the time spent on the service call represents the slope of the graph. We can find the slope of the graph by taking any two points on the line and calculating the change in y (total amount) divided by the change in x (time spent on the service call).

Looking at the graph, we can choose two points: (2, 130) and (8, 370). The change in y is:

370 - 130 = 240

And the change in x is:

8 - 2 = 6

Therefore, the slope (rate of change) of the graph is:

240/6 = 40

So the rate of change in the total amount charged with respect to the time spent on the service call is $40 per hour.

Therefore, the correct option is $40 per hour.

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A rectangular floor with a length of 14 ft and a width of 6 ft, square tiles with an edge length of 3/4 ft, a total of 144 tiles can fit.

To determine how many square tiles can fit in a rectangular floor, we need to calculate the total number of tiles that can fit both horizontally and vertically.

Given:

Length of the rectangular floor = 14 ft

Width of the rectangular floor = 6 ft

Edge length of square tile = 3/4 ft

First, let's calculate the number of tiles that can fit horizontally:

Length of the rectangular floor / Edge length of square tile = 14 ft / (3/4 ft) = 14 ft × (4/3 ft) = 56/3 ft

Since we want a whole number of tiles, we need to round down or take the floor value:

Number of tiles horizontally = floor(56/3) = 18 tiles

Next, let's calculate the number of tiles that can fit vertically:

Width of the rectangular floor / Edge length of square tile = 6 ft / (3/4 ft) = 6 ft × (4/3 ft) = 24/3 ft

Again, we round down or take the floor value:

Number of tiles vertically = floor(24/3) = 8 tiles

To find the total number of tiles, we multiply the number of tiles horizontally by the number of tiles vertically:

Total number of tiles = Number of tiles horizontally × Number of tiles vertically = 18 tiles × 8 tiles = 144 tiles

Therefore, in a rectangular floor with a length of 14 ft and a width of 6 ft, square tiles with an edge length of 3/4 ft, a total of 144 tiles can fit.

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❥\(\Large\pmb{ \underline {\tt Answer}}\)

#1

a + b • 3 = 3a + 3b

No

Actual equation formed:-

a + 3b = 3a + 3b

#2

Yes

#3

a + b • 3 = a + 3b

Yes

#4

a + 3b • 3= 3a + 6b

No

Actual equation formed:-

a + 9b

#5

a + 3b • 3 = a + 9b

Yes

Rule applies:-

BODMAS

B - brakets

O - on/off

D- divide

M - multiply

A - add

S - subtract

━━━━━━━━━━━━━━━━━━

After considering the given set of options we conclude that a large sample was used in the evaluation, which means the correct option is Option A.

1/2 is the evaluated expected probability for the given case under the condition that when the die was rolled an even number came out with face number 1 out of 6.

In the event that the cube was rolled 20 times, an even number came up 15 times, or 3/4 of the time. Now the same cube was again rolled 100 times, an even number came up on the recent throw which showed 51 times even, or almost 1/2 the time.

Therefore we can say that the actual results are closer to the expected probability of 1/2 when rolling the cube 100 times because a larger sample size was used.
Hence we are dealing with  larger  sample size, this means that the actual results will be much closer to the expected probability.
This is due to the law of large numbers which states that as the sample size increases, the average of the results will get closer and closer to the expected value .
Therefore, option (a) is correct.
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