What number should be the exponent on the 10 so that the two numbers are equivalent? 75.6 - 10% = 0.00756 y = -3 C y = 3 c y y = 4 y = 4 =

Proportion = 0.2119

P (X is less than or equal to 0.18) = P [(X-μ)/ sigma is less than or equal to (0.18-0.22)/ 0.05] = P(Z is less than or equal to -0.80). Using z-table proportion = 0.2119

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Answer:

8.2 units (nearest tenth)

Step-by-step explanation:

Distance between two points

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

where (x₁, y₁) and (x₂, y₂) are the two points.

Given points:

Substitute the given points into the distance formula and solve for d:

[tex]\implies d=\sqrt{(4-6)^2+(-1-7)^2}[/tex]

[tex]\implies d=\sqrt{(-2)^2+(-8)^2}[/tex]

[tex]\implies d=\sqrt{4+64}[/tex]

[tex]\implies d=\sqrt{68}[/tex]

[tex]\implies d=8.2 \; \sf (nearest\;tenth)[/tex]

Therefore, the distance between the two given points is 8.2 units to the nearest tenth.

Given a sample of the size, measured in square feet, of 17 faculty offices.

1) Mean

To calculate the mean of the sample you have to add all observations of the data set and divide it by the sample size:

The mean square footage is 131.5 ft²

2) Median

To determine the median of the data set, first, you have to calculate the position of the median, following the formula:

The sample size is n=17, then the position of the median is

The median corresponds to the ninth observation of the data set.

Next, you have to order the data set from least to greatest:

102, 104, 107, 110, 113, 119, 120, 123, 124, 127, 136, 142, 154, 155, 155, 159, 185

Count the ninth observation from the left.

The median of the data set is Me= 124 ft²

The cost of the fare based on the information is $16.32.

Amount for the fare = $12.75

Tip for the driver = 20% = 20% × $12.75 = $2.55

Tax rate = 8% = 8% × $12.75 = $1.02

Therefore the total amount will be:

= Cost of fare + Tip + Tax

= $12.75 + $2.55 + $1.02

= $16.32

The cost is $16.32. This illustrate the concept of addition.

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7 cows will eat all the grass on the farm in 28 days

17 cows eat all the grass on the farm in 10 days

15 cows eat all the grass in the farm in 12 days

We can see a relationship between the number of cows and the number of days. A reduction of 2 cows leads to an increase in 2 days for the cows to eat the grass.

As a result, when we reduce the cows by 4 the increase in the number of days will be 8.

Hence, to reduce the cows from 15 to 7 we will reduce the number of cows by 8 resulting in an increase in 16 days for the grass on the farm to be eaten up

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(a) Let "X" be the random variable that represents the time in minutes required to assemble the product.

(b) The random variable may assume the values in the interval (0, ∞).

(c) The random variable "X" is continuous in nature.

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Let:

A = Rolling an odd number

B = Rolling a 5

N = Number of possible outcomes

so:

Answer: y = 1

Step-by-step explanation:

Given

7 + y = 5(2y - 1) + 3y ← distribute and simplify right side

7 + y = 10y - 5 + 3y

7 + y = 13y - 5 ( subtract y from both sides )

7 = 12y - 5 ( add 5 to both sides )

12 = 12y ( divide both sides by 12 )

1 = y

The equation of a function that results in a graph that shows exponential decay is f(x) = 3(0.7)ˣ

An exponential function is represented as

f(x) = abˣ

Where

A function that represents an exponential decay would have a rate less than 1

This is represented as b <1

From the list of options, we have

f(x) = 3(0.7)ˣ

By comparing f(x) = 3(0.7)ˣ and f(x) = abˣ, we have

b = 0.7

0.7 is less than 1

Hence, the exponential decay function is f(x) = 3(0.7)ˣ

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Answer:

7/5

Step-by-step explanation:

1/2 + 1/5

probability that at least one of the two students fail is 7/5

Answer:

  A: 15%

  B: 43%

  C: yes

Step-by-step explanation:

You want the percentages of students who failed the exam, given that they (A) did, or (B) did not complete the exam review. You also want to know if this indicates an association between failing and reviewing.

Let F represent the event "failed the exam." Let R represent the event "completed the exam review." R' will be the event "did not complete the review."

The probability is ...

  P(F|R) = P(F&R) / P(R)

  P(F|R) = 0.10/0.65 = 2/13 ≈ 15%

About 15% failed who completed the review.

  P(F|R') = P(F&R') / P(R')

  P(F|R') = 0.15/0.35 = 3/7 ≈ 43%

About 43% failed who did not complete the review.

If the events "Failed the exam" and "Completed the review" were independent, then the probability of one would not be conditional upon the other. Here, the probability of failing is clearly different for those who completed the review, so there is an association between failing the exam and completing the exam review.

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Answer:

w = 35

Step-by-step explanation:

29 + 17w = 624

subtract 29 from both side

17 w = 595

divide both sides by 17

w = 35

Answer:

Step-by-step explanation:

Answer:

They are congruent by SAS:

Side: AB = CB

Angle: ∠ABD = ∠CBD

Side: BD = BD

Explanation:

Two triangles are congruent if they have the same interior angles and the same length of their corresponding sides.

If two of the angles are equal, we can say that all the interior angles are equal.

So, based on the given information we get:

1. AC ⊥ BD means that AC is perpendicular to BD, therefore,

∠ADB = ∠CDB = 90°

2. It is given that ∠A = ∠C

3. Since both of their interior angles are equal, we can say that all the interior angles are equal and:

∠ABD = ∠CBD

4. The triangle ABC is isosceles because two of their interior angles are equal, therefore AB = CB

5. BD = BD because it is the same segment.

6. By SAS (Side-angle-Side) we can say that ΔABD = ΔCBD

Because the side AB is equal to side CB, the angle ABD is equal to angle CBD, and the side BD is equal to itself.

Answer:

Step-by-step explanation:

[tex]5(2-x)-10=25-2(3x+40)\\\\10-5x-10=25-6x-80\\\\-5x=-6x-55\\\\-5x+6x=-55\\\\x= -55 [/tex]

Answer:

x = -55

Step-by-step explanation:

Hello!

We can solve for x by isolating the variable.

The value of x is -55.

Given that the batters were 7, 14,6,4,5 and 6 then to find the average, you add the batters and divide by their number

Here you notice that the average is 7, so the coach's statement is true.

Your answer is , No;the mean of her strikeouts is 7

It is enough for him to use a simple random sample of 172 cars.

It is required that there are at least 10 successes and 10 failures to test a hypothesis that involves a proportion p in a sample of size n.

Following conditions are required for it:

1) np ≥ 10

2) n (1-p) ≥ 10

p = 6% = 0.06

n = 172

So, there are at least 10 successes and 10 failures in the 172 cars sample, it is enough for him to use a simple random sample of 172 cars.

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Answer:

+3, -1

Step-by-step explanation:

17 + 3 = 20

20 - 1 = 19

19 + 3 = 22

22 - 1 = 21

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If Andrew earns 30% on all sales plus a retainer of $125 per week and If he earns $893 in one week, then the value of the his sales for that week is $2560.

The total amount he earned = $893

The amount of retainer he earned = $125

The percentage he earned = 30%

30% of the sales = The total amount he earned - The amount of retainer he earned

Substitute the values in the equation

= 893-125

= $768

Consider the total sales as x

Then,

x × (30/100) = 768

0.3x = 768

x = 768/0.3

x = $2560

Hence, if Andrew earns 30% on all sales plus a retainer of $125 per week and If he earns $893 in one week, then the value of the his sales for that week is $2560.

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Answer:

1.75x + 1.25y >= 280

Step-by-step explanation:

1.75x + 1.25y >= 280

Answer: Yes

Step-by-step explanation: 250-250

An outlier is when some of the data is spread farther away from the rest of the data. It is far off from other data

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Here, we want to drop a box plot on the number line given the listed numbers

We have the box plot as follows

The listing of the numbers is the actual way the numbers on the box plot will be listed from left to right

We have this as follows;

The slopes formed by each of the pairs of points are given as follows:

The slope is equivalent to the rate of change, hence, given two points, the slope is calculated as the change in y, also called rise, of these two points divided by the change in x, also called run.

For the first case, the points are:

(2, 11.9) and (4, 10.5)

Hence:

The slope is:

m = -1.4/2 = -0.7.

The other slopes are calculated as follows:

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The length and width of the rectangle are 5.5 inches and 10.5 inches.

So, the dimensions of the rectangle:

Substitute the values in the formula as follows:

Therefore, the length and width of the rectangle are 5.5 inches and 10.5 inches.

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Answer:

(a)  19.6 ms⁻¹

(b)  2 s

(c)  9.8 ms⁻¹

(d)  4 s

Step-by-step explanation:

Constant Acceleration Equations (SUVAT)

[tex]\boxed{\begin{array}{c}\begin{aligned}v&=u+at\\\\s&=ut+\dfrac{1}{2}at^2\\\\ s&=\left(\dfrac{u+v}{2}\right)t\\\\v^2&=u^2+2as\\\\s&=vt-\dfrac{1}{2}at^2\end{aligned}\end{array}} \quad \boxed{\begin{minipage}{4.6 cm}$s$ = displacement in m\\\\$u$ = initial velocity in ms$^{-1}$\\\\$v$ = final velocity in ms$^{-1}$\\\\$a$ = acceleration in ms$^{-2}$\\\\$t$ = time in s (seconds)\end{minipage}}[/tex]

When using SUVAT, assume the object is modeled as a particle and that acceleration is constant.

Acceleration due to gravity = 9.8 ms⁻².

When the ball reaches its maximum height, its velocity will momentarily be zero.

Given values (taking up as positive):

[tex]s=19.6 \quad v=0 \quad a=-9.8[/tex]

[tex]\begin{aligned}\textsf{Using} \quad v^2&=u^2+2as\\\\\textsf{Substitute the given values:}\\0^2&=u^2+2(-9.8)(19.6)\\0&=u^2-384.16\\u^2&=384.16\\u&=\sqrt{384.16}\\\implies u&=19.6\; \sf ms^{-1}\end{aligned}[/tex]

Therefore, the initial speed is 19.6 ms⁻¹.

Using the same values as for part (a):

[tex]\begin{aligned}\textsf{Using} \quad s&=vt-\dfrac{1}{2}at^2\\\\\textsf{Substitute the given values:}\\19.6&=0(t)-\dfrac{1}{2}(-9.8)t^2\\19.6&=4.9t^2\\t^2&=\dfrac{19.6}{4.9}\\t^2&=4\\t&=\sqrt{4}\\\implies t&=2\; \sf s\end{aligned}[/tex]

Therefore, the time taken to reach the highest point is 2 seconds.

As the ball reaches its maximum height at 2 seconds, one second before this time is 1 s.

Given values (taking up as positive):

[tex]u=19.6 \quad a=-9.8 \quad t=1[/tex]

[tex]\begin{aligned}\textsf{Using} \quad v&=u+at\\\\\textsf{Substitute the given values:}\\v&=19.6+(-9.8)(1)\\v&=19.6-9.8\\\implies v&=9.8\; \sf ms^{-1}\end{aligned}[/tex]

The velocity of the ball one second before it reaches its maximum height is the same as the velocity one second after.

Proof

When the ball reaches its maximum height, its velocity is zero.

Therefore, the values for the downwards journey (from when it reaches its maximum height):

[tex]u=0 \quad a=9.8 \quad t=1[/tex]

(acceleration is now positive as we are taking ↓ as positive).

[tex]\begin{aligned}\textsf{Using} \quad v&=u+at\\\\\textsf{Substitute the given values:}\\v&=0+9.8(1)\\\implies v&=9.8\; \sf ms^{-1}\end{aligned}[/tex]

Therefore, the velocity of the ball one second before and one second after it reaches the maximum height is 9.8 ms⁻¹.

From part (a) we know that the time taken to reach the highest point is 2 seconds.  Therefore, the time taken by the ball to travel from the highest point to its original position will also be 2 seconds.

Therefore, the total time taken by the ball to return to its original position after it is thrown upwards is 4 seconds.

The greatest common factor is  5 .

If you factor it out, the expression becomes        5 (4x + 7y) .

Answer: 55x^1 y^1

Step-by-step explanation:
Add 20+35= 55
x & y can't stand by it's self, so x^1 and y^1
So you take those answers and you got 55x^1 y^1
You must keep it in letters in alphabetic order or it's considered wrong.

Step 1

Given; A graph

Required; To find f(-4)

Step 2

The graph at x=-4 has a removable discontinuity. Therefore we can then conclude that f(-4) is undefined.

Hence, f(-4) is undefined

A removable discontinuity is a point on the graph that is undefined or does not fit into the rest of the graph.

Answer: The image and the preimage have the same orientation.

Answer:

The image and the preimage have the different orientation.

Step-by-step explanation:

i

took

the

test

Answer:

Step-by-step explanation:

two angles are a linear pair, and one has twice the measure of the other. Find the smaller angles measure

linear pair = 180°

180 : 3 = 60° (smaller angle)

60° x 2 = 120° (bigger angle)

120 is twice 60 and the sum is 180°

the answer is good