URGENT PLZ BE QUICK!!

Pauline is buying a shirt that was originally priced at $15. The star has a today - only discount of 25%. What is today’s price for the shirt?

Answers

Answer 1

Answer:

$11.25

Step-by-step explanation:

.25x15=3.75

15-3.75=11.25


Related Questions

(1) How many distinct permutations can be made from the letters of the word INFINITY?
(2) How many of these permutations starts with the letter Y?
calculate the following expression:

Answers

The word "INFINITY" has eight letters. To find out the number of distinct permutations that can be made from the word "INFINITY," we will use the formula for permutation. The formula is:$$P(n,r) = \frac{n!}{(n-r)!}$$Where n is the total number of items and r is the number of items taken at a time.

Using the formula, we get:\($$P(8,8) = \frac{8!}{(8-8)!}$$$$P(8,8) = \frac{8!}{0!}$$$$P(8,8) = 8!$$$$P(8,8) = 40,320$$\). There are 40,320 distinct permutations that can be made from the letters of the word INFINITY. To find out the number of permutations that start with the letter Y, we will treat Y as a fixed letter at the beginning. Then we will find the number of permutations of the remaining seven letters.

This can be done using the same formula as before. But this time, we will use n = 7 and r = 7. The formula becomes:\($$P(7,7) = \frac{7!}{(7-7)!}$$$$P(7,7) = \frac{7!}{0!}$$$$P(7,7) = 7!$$$$P(7,7) = 5,040$$\). Therefore, there are 5,040 permutations that start with the letter Y.

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PLEASE HELP!
Find the surface area of the cylinder with diameter 20 in. and height 2 in. Use 3.14 for
pi.

Answers

Answer:

\(\boxed {\boxed {\sf SA= 753.6 \ in^2}}\)

Step-by-step explanation:

The surface area of a cylinder is found using this formula.

\(SA=2 \pi rh+ 2 \pi r^2\)

We know the diameter is 20 inches and the height is 2 inches. We must find the radius.

The radius is half the diameter. r= d/2 r= 20 in /2= 10 in

Now we know that:

\(r= 10 \ in \\h= 2 \ in\)

Substitute the values into the formula. Also, plug 3.14 in for pi.

\(SA=2 (3.14)(10 \ in)(2 \ in)+ 2 (3.14)(10 \ in)^2\)

Solve according to PEMDAS: parentheses, exponents, multiplication, division, addition, and subtraction.

Solve the exponent.

(10 in)²= 10 in * 10 in= 100 in²

\(SA=2 (3.14)(10 \ in)(2 \ in)+ 2 (3.14)(100 \ in^2)\)

Multiply all the numbers together.

\(SA=2 (3.14)(20 \ in^2)+ 2 (3.14)(100 \ in^2)\)

\(SA=125.6 \ in^2+628 \ in^2\)

Add.

\(SA= 753.6 \ in^2\)

The surface of the cylinder is 753.6 square inches.

An analyst must decide between two different forecasting techniques for weekly sales of roller blades: a linear trend equation and the naive approach. The linear trend equation is \( F_{t}=127+2.1 t \

Answers

When forecasting techniques are being considered, an analyst must choose between two techniques for weekly sales of roller blades. The two techniques are linear trend equation and naive approach. The linear trend equation is given as \(F_t\) = 127 + 2.1t.

Linear Trend Equation: Linear trend equation is one of the forecasting techniques used to predict trends and estimate the relationship between variables. It is calculated as\(F_t\) = a + bt, where \(F_t\)represents the forecasting value, b represents the slope and a represents the y-intercept.

The equation is used to forecast values for the dependent variable based on independent variables. The linear trend equation is used to forecast future values and interpret the relationship between variables. The equation can be used to forecast the trend of data that shows a linear trend or a straight line, as well as predict values for future periods in time.

Naive Approach : The Naive approach is one of the simplest forecasting techniques used to make predictions. This method assumes that the best estimate of a future value is the current value. It is based on the belief that the most recent value of a time series provides the best estimate of the future.

In conclusion, the analyst must choose between two forecasting techniques, linear trend equation and naive approach. The linear trend equation is based on estimating the relationship between variables, while the Naive approach assumes that the best estimate of a future value is the current value.

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Help greatly appreciated.

Find the values of x and y. I need help knowing which formula to use and what to plug into the formula. Thank you.

Help greatly appreciated. Find the values of x and y. I need help knowing which formula to use and what

Answers

The value of x is 4√6. The value of y is 4√2.

What are similar triangles?

If two triangles have the same ratio of corresponding sides and an equal pair of corresponding angles, they are similar. When two or more figures have the same shape but differ in size, they are referred to as similar figures.

Consider △ABC:

Height = AC = x, Hypoteneous = BC = 4+8 = 12.

Consider △ADC:

Height = DC = 8, Base = AD = y, Hypoteneous =  AC = x

Consider △ABD:

Height = AD = y, Base = 4.

The triangle ABC is similar to ADC, and ABC is similar to ABD. Since all have one right angle and one angle is common.

The ratio of the corresponding sides of similar triangles is constant.

Consider △ABC and △ADC:

AC/DC = BC/AC

x/8 = 12/x

x² = 12×8

x = 4√6.

Since ABC is similar to ADC and ABC is similar to ABD. Then ADC is similar to ABD.

Consider △ADC and △ABD:

DC/AD = AD/BD

8/y = y/4

y² = 4×8

y = 4√2

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Is (2,1) a solution to y> 2x-1

Answers

1>2*2-1
1>4-1
1>3
False So No

Write the equation of the line using slope-intercept form
with the following information:

( 1,9) and (2,3)

Answers

Answer:

its 1290 ans there is the awer

The tallest building in the United States is the Willis Tower
located in Chicago, Illinois. The Willis Tower is 1,451 feet
tall. The tallest building in the world is Taipei 101 located in
Taipei, Taiwan. Taipei 101 is 1,671 feet tall. How many feet
taller is Taipei 101 than the Willis Tower?

Answers

Answer:

220

Step-by-step explanation:

1,671 - 1,451 = 220

hope it helps :)

mark brainliest!!!

Triangle $ABC$ has its vertices $A$, $B$, and $C$ on the sides of a rectangle 4 units by 5 units as shown. What is the area of triangle $ABC$ in square units?

Answers

Answer:

10 square units.

Step-by-step explanation:

It is given that triangle ABC has its vertices A, B, and C on the sides of a rectangle 4 units by 5 units.

Height of triangle = 4 units

Base of triangle = 5 units

We need to find the area of triangle.

Area of triangle \(=\dfrac{1}{2}\times base \times height\)

Substitute base = 5 and height = 4 in the above formula.

Area of triangle \(=\dfrac{1}{2}\times 5\times 4\)

Area of triangle \(=\dfrac{20}{2}\)

Area of triangle \(=10\)

Therefore, the area of triangle ABC is 10 square units.

Answer:

9

Step-by-step explanation:

Calculate (8.42 x 109) − (2.35 x 108).

Answers

Answer:

Step-by-step explanation:

663.98

Answer: 663.98

Step-by-step explanation:

(8.42*109)=917.78

(2.35*108)=253.8

917.78-253.8=663.98

Write an equation in point slope form of the line that passes through the point -4, 5 and has the slope of one.

Answers

Answer:

y - 5 = x + 4

Step-by-step explanation:

Use point slope form, y - y1 = m(x - x1) where m is the slope and (x1, y1) is a point on the line

Plug in the given point and slope:

y - y1 = m(x - x1)

y - 5 = 1(x + 4)

Simplify:

y - 5 = x + 4

So, the point slope form of the line is y - 5 = x + 4

Andre owns a condominium with a value of $155,000. He has a stock portfolio worth $8,100. He owes $3,300 on his car, which is valued at $9,100. He has $7,600 in student loans to repay. He has a credit card balance of $4,327. He also has $2,600 in a bank account. Construct a net worth statement to find Andre's net worth.

Answers

Using  net worth statement, Andre's net worth is $159,573.

How to Construct a net worth statement to find Andre's net worth.

Andre's net worth can be calculated by subtracting his total liabilities from his total assets.

Total assets = $155,000 (condominium) + $8,100 (stock portfolio) + $9,100 (car value) + $2,600 (bank account) = $174,800

Total liabilities = $3,300 (car loan) + $7,600 (student loans) + $4,327 (credit card balance) = $15,227

Net worth = Total assets - Total liabilities = $174,800 - $15,227 = $159,573

Therefore, Andre's net worth is $159,573.

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A nationwide survey of a random sample of teenagers asked
whether or not they play sports. The survey concluded that 53%
play at least one sport. Use this information to predict how many
students in a school with 2,000 teenage students play at least one
sport.

Answers

Answer:

1060 students

Step-by-step explanation:

Calculate minimum and maximum frequency for acoustic
and optic mode.
( short question (

Answers

The specific range depends on the material properties and the energy levels involved.

The minimum and maximum frequencies for the acoustic and optic modes depend on the specific system or material under consideration. However, I can provide some general information.

Acoustic Mode:

The acoustic mode refers to the propagation of sound waves or vibrations in a material. In a solid, the acoustic mode can have different types, such as longitudinal and transverse modes.

The minimum frequency for the acoustic mode is typically determined by the size and physical properties of the material. In general, it can be close to zero for macroscopic objects or materials with low elasticity.

The maximum frequency for the acoustic mode depends on factors such as the speed of sound in the material and the characteristic dimensions of the system. It can range from a few kilohertz to several gigahertz.

Optic Mode:

The optic mode is related to the interaction of light with a material. It typically refers to the vibrations of charged particles (such as electrons) in a solid or the oscillations of electric or magnetic fields associated with photons.

The minimum frequency for the optic mode is typically determined by the energy gap between electronic states in the material. For example, in a semiconductor, the minimum frequency is usually in the infrared range.

The maximum frequency for the optic mode is not strictly defined, as it can extend into the terahertz, infrared, visible, ultraviolet, X-ray, and even gamma-ray regions. The specific range depends on the material properties and the energy levels involved.

It's important to note that these frequency ranges are general guidelines and can vary depending on the specific system or material being studied.

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A parallelogram has vertices A(-2,1), B(3,2), C(4,6), D(-1,5). At what point do the diagonals intersect? PLZZ HELPPPP

A. (1,3 1/2)
B. (2,3 1/2)
C. (2, 4 1/2)
D. (1 1/2,4)

Answers

Answer:

I believe the A goes with the B the B goes with D that al I know soryy

Does someone mind helping me with this problem? Thank you!

Does someone mind helping me with this problem? Thank you!

Answers

Answer:

72

Step-by-step explanation:

;)

a square sheet of paper has area $15\text{ cm}^2$. the front side is white and the back side is black. a corner of the sheet is lifted and placed so that the crease is at a $45^\circ$ angle. if the fold is such that the visible black area is equal to the visible white area, how many centimeters long is the crease? express your answer in simplest radical form.

Answers

The crease is \($x = \sqrt{15}\text{ cm}$\) long.

Let $x$ be the length of the crease. Then, the visible white area is a triangle with base of length $x$ and height of \($x\sqrt2$.\) The visible black area is also a triangle with the same base and height. Therefore, we have the equation

\($\frac{x^2\sqrt2}{2} = \frac{15}{2}$\)

Solving for $x$, we get

\(x^2=\sqrt{15}\)

Therefore, the crease is \($x = \sqrt{15}\text{ cm}$\) long.

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ERROR ANALYSIS Describe and correct the error in identifying congruent triangles. TUV=XYZ by the SSS Congruence Theorem.​

ERROR ANALYSIS Describe and correct the error in identifying congruent triangles. TUV=XYZ by the SSS

Answers

Answer:

The letters for XYZ are in the wrong order.

The correct statement should be \(\triangle TUV \cong \triangle ZYX\)

============================================

Further Explanation:

The order of the letters matters when writing congruence statements.

The claim is that \(\triangle TUV \cong \triangle XYZ\)

The first two letters of each are "TU" and "XY" in that order.

But notice how TU has a single tickmark, while XY has a double tickmark. The two sides are clearly different.

--------

Instead, the statement should be: \(\triangle TUV \cong \triangle ZYX\) because of the following three facts:

TU = ZY  (single tickmark)UV = YX  (double tickmark)TV = ZX (triple tickmark)

Notice that:

TU and ZY are the 1st two letters of TUV and ZYXUV and YX are the last two letters of TUV and ZYXTV and ZX are the 1st and 3rd letters of TUV and ZYX

how large a sample would be required in order to estimate the fraction of people who black out at 6 or more gs at the 98% confidence level with an error of at most 0.03 ? round your answer up to the next integer.

Answers

To estimate the fraction of people who black out at 6 or more gs at 98% confidence level and an error of at most 0.03, a sample size of 1079 is required using the formula n = (2.33² * 0.5 * (1-0.5)) / 0.03², rounded up to the nearest integer.

To determine the sample size required to estimate the fraction of people who black out at 6 or more gs with an error of at most 0.03 and a 98% confidence level, we need to use the formula

n = (z² * p * (1-p)) / E²

where

n is the sample size

z is the z-score for the desired confidence level (2.33 for 98% confidence)

p is the estimated proportion of people who black out at 6 or more gs (unknown)

E is the maximum error (0.03)

We don't know the estimated proportion p, but we can assume that it is 0.5, which is the value that will give the maximum sample size. So, substituting the values into the formula, we get

n = (2.33² * 0.5 * (1-0.5)) / 0.03² = 1078.8

Rounding up to the nearest integer, we get a sample size of 1079. Therefore, a sample size of 1079 is required to estimate the fraction of people who black out at 6 or more gs at the 98% confidence level with an error of at most 0.03.

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14. In the following figure, M is the midpoint of
(FA) and (MA) and (MB) are the tangents issued
from M to the circle(C).
F
M
B
(C)
question: Show that ABF is a right triangle.​

14. In the following figure, M is the midpoint of(FA) and (MA) and (MB) are the tangents issuedfrom M

Answers

Answer:

angle OAM and OBM are right angles because tangents form right angles with radii.

AO=BO and MA=MB

Quadrilateral MAOB =360 degrees

so angles AOB and AMB=90 degrees each

angle MBF=90 degrees

M is the midpoint of FA so MA=MF

MB=MF

Triangle MBF is a right triangle because angle BMF is 90 degrees and  MB=MF

What is the value of b in the triangle shown below?
o -4 in
o 4 in
o +-4 in
o no solution

What is the value of b in the triangle shown below? o -4 ino 4 ino +-4 ino no solution

Answers

Answer:

b= 4 in.

Step-by-step explanation:

Ok. So the area of a triangle is base * height divided by 2.

So, the base is b and the height is 3b.

b*3b= 3b^2.

Now, divide that by 2.

(3b^2)/2.

Now, we know what the area is already- 24 in.^2. So, let's set the area expression that I found earlier equal to this area, since they're the same.

(3b^2)/2 = 24

3b^2 = 48

b^2 = 16

Ok. Let's stop here. Now, we square root both sides to obtain b, but we are presented with a problem here. B can equal both 4 and -4 right? Since -4*-4=16 and 4*4=16. However, it is impossible for a 2d shape to have negative measurements. So, the answer is 4.

Answer:

+4 in

Step-by-step explanation:

A= 1/2 x b x h

24=1/2 x b x 3b

b2=16

b=+4 or -4(N/A)

Laws and phenomena of nature, naturally occurring substances, abstract mathematical formulas, and ideas are eligible to be patented. True False

Answers

Answer:

False

Step-by-step explanation:

Laws of Nature. Laws of nature, natural phenomena, and naturally-occurring products are not patentable.

the relations or order of phenomena in the world that holds, under a stipulated set of conditions, either universally or in a stated proportion of instances. (The notion is distinct from that of a natural law—i.e., a law of right or justice supposedly derived from nature.)

find the critical value(s) and rejection region(s) for the type of z-test with level of significance . include a graph with your answer. right-tailed test, a=0.03.

Answers

Answer:

c

Step-by-step explanation:

The red line represents the critical value, and the shaded region on the right-hand side of the red line represents the rejection region. If the calculated test statistic is greater than the critical value of z, which is 1.88 in this case, we will reject the null hypothesis.

The critical value(s) and rejection region(s) for the type of z-test with a level of significance a = 0.03 and a right-tailed test are as follows :Step 1: Determine the critical value of  zThe critical value is calculated by using the normal distribution table and the level of significance. A right-tailed test will have a critical value of zα. For a level of significance of 0.03, we will look for the z-value that corresponds to 0.03 in the normal distribution table.Critical value for a = 0.03 is z = 1.88 (approx).Step 2: Determine the Rejection Region The rejection region for a right-tailed test is defined as any z-value that is greater than the critical value. That is, if the test statistic is greater than 1.88, we reject the null hypothesis at the 0.03 level of significance, and if it is less than or equal to 1.88, we fail to reject the null hypothesis.Therefore, the rejection region for a right-tailed test with a level of significance of 0.03 is as follows:Rejection Region: Z > 1.88  OR  Z ≤ -1.88Graph: The graph for the given values will be as follows:The red line represents the critical value, and the shaded region on the right-hand side of the red line represents the rejection region. If the calculated test statistic is greater than the critical value of z, which is 1.88 in this case, we will reject the null hypothesis.

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when conducting a statistical hypothesis test, what is it that we are actually doing?
O Determining whether the research hypothesis is true O Evaluating the direction of the research hypothesis O Falsifying the null hypothesis O Specifying a probability that H, is equal to zero

Answers

Answer: 12

Step-by-step explanation:

Linda had 90 fliers to post around town. Last week, she posted 1/5 of them. This week, she posted 1/3 of the remaining fliers. How many fliers has she still not posted?

Answers

The number of fliers that she has still not broadcasted will be 48 fliers.

What is Algebra?

Algebra is the study of ideational characters, while logic is the manipulation of all those opinions.

Linda had 90 fliers to post around town. Last week, she posted 1/5 of them. Then the number of fliers staying is given as,

⇒ (1 - 1/5) x 90

⇒ (4/5) x 90

⇒ 72 fliers

This week, she posted 1/3 of the remaining fliers. Then the number of fliers that she has still not broadcasted is given as,

⇒ (1 - 1/3) x 72

⇒ (2/3) x 72

⇒ 48 fliers

The number of fliers that she has still not broadcasted will be 48 fliers.

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let me know i need asap thank you

let me know i need asap thank you

Answers

Answer:

Step-by-step explanation:

It might be A or D I’m not for sure which one it is.

In a survey of 349 people, a pet food manufacturer found that 145 owned a dog but not a cat, 60 owned a cat but not a dog, and 71 owncd neither a dog or a cat. (a) How many owned both a cat and a dog?

Answers

The number of people who owned both a cat and a dog is 73.

We need to calculate how many people owned both a cat and a dog. The number of people who owned a dog and/or a cat is:

Total = dog-only + cat-only + dog-and-cat + neither

Total = 145 + 60 + dog-and-cat + 71

Total = 276 + dog-and-cat

So, the number of people who owned both a cat and a dog (dog-and-cat) is:

dog-and-cat = Total - 276

dog-and-cat = 349 - 276

dog-and-cat = 73

However, this number is the total of those who own both. The answer to the question asks how many owned both a cat and a dog.

So:

dog-and-cat = dog-only + cat-only + dog-and-cat

dog-and-cat = 145 + 60 + dog-and-cat

73 = 145 + 60 + dog-and-cat

dog-and-cat = 73 - 205

dog-and-cat = -132

Hence, 132 people neither own a dog nor a cat. So, the number of people who owned both a cat and a dog is:

dog-and-cat = Total - (dog-only + cat-only + neither)

dog-and-cat = 349 - (145 + 60 + 71)

dog-and-cat = 349 - 276

dog-and-cat = 73

Therefore, the number of people who owned both a cat and a dog is 73.

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help. pls.
-photo attached !

Find the measures of the numbered angles.


(the angles i need to find)

<1 _?
<2 _?
<3 _?
<4 _?
<5 _?
<6 _?
<7 _?
<8 _?

help. pls.-photo attached ! Find the measures of the numbered angles.(the angles i need to find) &lt;1

Answers

Answer:

<1=75°[corresponding angles are equal]

<2=180-<1=(180-75)°=105°[sum of st.angles is supplementary]

<3=<2=105°[Vertically opposite angles are equal]

<4=75°[Alternate angles are equal]

<6=<2=105°[Corresponding angles are equal]

<7=<6=105°[Vertically opposite angles are equal]

<8=75°[Vertically opposite angles are equal]

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please answer quickly!! what is the exact value of x and y? please leave an answer if you’re going to comment!! (i’ve posted this 3 times)

please answer quickly!! what is the exact value of x and y? please leave an answer if youre going to

Answers

To solve this problem

  ⇒ need to use the special right triangle theorem

    ⇒ 30-60-90 triangle theorem (look at diagram attached for the property)

(we can use this theorem because the square on one of the angles indicates that the angle is 90 degrees. The other angle is indicated as 60 degrees. All the angles of a triangle should add up to 180, so the last angle is 30 degrees)

Using the theorem:

the side facing opposite the 60-degree angle is equal ⇒ \(x\sqrt{3}\)

            \(x\sqrt{3} =17\sqrt{3} \\x = 17\)

the side facing opposite the 90-degree angle is twice the value of x  

             \(y = 2x = 2 * 17 =34\)

Answers:

  x = 17 and y = 34

Hope that helps!

please answer quickly!! what is the exact value of x and y? please leave an answer if youre going to
X=17 y=34

EXPLANATION:According to the 30 60 90 rule the Y value would be double the x and the x in the longer leg would be the short leg value

Find the volume of the cone. Write your answer in terms of pi.

Find the volume of the cone. Write your answer in terms of pi.

Answers

7800pi mm^3 or about 24604 mm

Scientists studying the Belize Barrier Reef notice that the mantis shrimp population is declining, so they exhaustively census the population and find that the population size is 475 individuals. This species lives in a stable environment without pulsed reproduction. They continue to monitor the population and calculate an intrinsic rate of increase of -0.10. What will the population size be after 5 years?

Answers

The population size of mantis shrimp will be approximately 266 individuals after 5 years.

The intrinsic rate of increase is an essential concept in population biology. It is the rate at which a population is growing at a particular moment in time. The population size after a particular period can be calculated using the intrinsic rate of increase with the help of this formula:

Nt = N0e^(rt)

where Nt is the future population size, N0 is the initial population size, r is the intrinsic rate of increase, and t is the time in years.

The population size of mantis shrimp is 475 individuals and the intrinsic rate of increase is -0.10.

We can calculate the population size after 5 years using the above formula as follows:

Nt = N0e^(rt)

Nt = 475 * e^(-0.10 * 5)

Nt = 475 * e^(-0.50)

Nt ≈ 266

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NO LINKS!! Explain your answer (show the support by showing the changes in x and y on your table). If the relationship is linear, inverse or exponential, write the equation. #9 Completa la siguiente sucesin y encuentra su regla general. -10, -5, ___, ___, 10,... Regla general: Por favor es urgente, no le entiendo muy bien Explain the significance of the following terms from this lesson. a. desert b. inflation The graph of the linear function is shown on the coordinate grid. (-4, 6). (1, -9) What is the y-Intercept of the graph of the linear function?A: -3B: -2C: -6 D: 6 stored procedures execute faster than an equivalent sql script because stored procedures are what? a current of 5.00 a flowed in a copper wire for 20.0 s. how many coulombs of charge passed through the wire in this time? Which of the following phenomena can only be explained by considering the wave nature of light? Select the correct answer below: - Reflection - Refraction - Interference - None of the above A rancher raises calves that need to be given vaccinations. To give the vaccinations, she must hire several helpers. The rancher knows that the vaccinations cost $20.50 per calf and estimates that the cost to pay helpers is $5 per calf.Which expressions represent the total cost of vaccinating x calves? Choose all that are correct.A.20.50x + 5.00xB. 20.50 +5.00 divided by xC.20.50 + 5.00 + xD.(20.50 + 5.00)xE. X divided by 20.50 + 5.00F. (20.50 + 5.00)x divided by x(PLEASE HELP ME I ONLY HAVE UNTIL TOMORROW TO GET THIS DONE. I have so many late assignments, i really just need someone to help me with some of these. for this, you dont have to answer #1, i can do that. i just need help with 2 and 3. Thank You! A Moving to another question will save this response. restion 21 S1 unit of angular acceleration is radians m/s row/s^2 Well A) Moving to another question will save this response. (i will give brainly)Since the vast majority of scientific statements have been proven wrong, is there any good reasons to believe in science? _____ refers to non-financial companies spreading out its activities in different currency zones in order to offset the currency losses in certain regions through gains in other regions. When a pure sample of KNO3(s) spontaneously dissolves in water at room temperature, the solution becomes quite cold to the touch. For this reaction the enthalpy of the solution is _____ and the entropy is _____. What does "decentralize" mean?Blockchain is technically decentralized. How do you think thiswill affect the role of central banks in the digital currencymarket? How has Nora been repaying her debts? The settlement at roanoke represented an early failure for the english to colonize. identify why it most likely failed. map of field: 12 in 15 inscale of map: 1 in = 3 ft What are the dimensionsof the actual field? Solve the following system of equations by graphing3x + y = 42x + 3y = 2 Let X1,,Xn be a random sample from a n(,2) population. (a) If is unknown and 2 is known, show that Z=n(X0)/ is a Wald statistic for testing H0:=0. (b) If 2 is unknown and is known, find a Wald statistic for testing H0:=0. how do nuclear, biological, and chemical weapons threaten international security?