4 tens and 3 hundredths as a decimal

Answer:

D

Step-by-step explanation:

865 increase 25% =

865 × (1 + 25%) = 865 × (1 + 0.25) = 1081.25

Answer:

C. 252 miles.

Step-by-step explanation:

Since we already know how many miles is driven for 10 gallons of gas, we only need to find 2.

Since 105 miles runs on 5 gallons, divide 105 by 5 to find out how many miles runs on 1 gallon.

105/5=21

Then, multiply that by 2 to find out how many miles run on 2 gallons of gas.

21x2=42.

Finally, add 42 to 210 to get the amount of miles that runs on 12 gallons of gas.

210+42=252

Answer:

The rate of change of function A is greater than the rate of change of function B

Step-by-step explanation:

\(\sf rate \ of \ change=\dfrac{change \ in \ y}{change \ in \ x}\)

Function A

For every increase of 1 unit in x-values, the y-values increase by 3 units.

\(\sf rate \ of \ change=\dfrac{3}{1}=3\)

Function B

For every increase of 1 unit in x-values, the y-values increase by 2 units.

\(\sf rate \ of \ change=\dfrac{2}{1}=2\)

As 3 > 2, the rate of change of function A is greater than the rate of change of function B

The length of the microorganism that measure 5μm is equivalent to 0.005 mm

It is the transformation of a value expressed in one unit of measurement into an equivalent value expressed in another unit of measurement of the same nature.

To solve this problem the we have to convert the units with the given information.

1mm is equal to 1000 μm

5μm * (1 mm/1000μm) = (5*1) / 1000 = 5/1000 = 0.005 mm = 5x10^-3 mm

The length of the microorganism that measure 5μm is equivalent to 0.005 mm

Learn more about unit conversion at: brainly.com/question/141163

#SPJ4

Answer:

-3

Step-by-step explanation:

4-7/1-0

1-4/2-1

-2-1/3-2

Answer:

x= -3

Step-by-step explanation:

you replace y with -2 as the output

then subtract the 7 on both sides to have '-9=3x'

divide by 3 on both sides

x= -3

Answer:

x=-3

Step-by-step explanation:

y=3(-3)+7

y=-9+7

y=-2

The surface area of the box is 954 in².

Option D is the correct answer.

We have,

The surface area of a rectangular prism is the sum of the areas of all its faces.

The box has six faces, and each face is a rectangle.

The top and bottom faces have dimensions of 24 inches by 15 inches,

So each has an area of:

24 in × 15 in

= 360 in²

There are two of these faces, so their combined area is:

2 × 360 in²

= 720 in²

The front and back faces have dimensions of 24 inches by 3 inches,

So each has an area of:

24 in × 3 in

= 72 in²

There are two of these faces, so their combined area is:

2 × 72 in²

= 144 in²

The left and right faces have dimensions of 15 inches by 3 inches, so each has an area of:

15 in × 3 in

= 45 in²

There are two of these faces, so their combined area is:

2 × 45 in² = 90 in²

Adding up all the face areas gives:

720 + 144 + 90

= 954 in²

Therefore,

The surface area of the box is 954 in².

Learn more about Prism here:

https://brainly.com/question/12649592

#SPJ1

Answer:

2 an a half

Step-by-step explanation:

4+4 is 8 an than you have 2 which is half of four

The perimeter of the rectangle can be expressed as 2x + 84/x in terms only of x.

The perimeter of the rectangle can be expressed as:

2x + 2y

In this case, x is the width and y is the length.

Since we know the area of the rectangle is 42 in², we can use the formula for the area of a rectangle to solve for the length,

y = 42 / x.

Substituting this into the expression for the perimeter, we get,

2x + 2(42/x).

This simplifies toL

2x + 84/x.

Thus, the perimeter of the rectangle is 2x + 84/x in terms only of x.

To know more about perimeter  refer here:

https://brainly.com/question/6465134#

#SPJ11

EXPLANATION

If we need to know what percent of 300 represent 51, the appropiate equation would be:

%= (51/300)*100

So, the best equation is 51 = p X 300

The expression is to be written in complete square method and the value will be equal to  (x + 5/2)² + 7/4.

The expression x² + 5x + 8 is a quadratic polynomial and a quadratic polynomial is one which can be written in the form ax² + bx + c; where a, b and c are constant values and x is the independent variable. Now in order to write the expression by using completing square method we write the polynomial as

x² + 5x + 8

We divide the coefficient of x that is 5 by 2 so we get

x² + (5/2)x + 8

Now, we add and subtract the square of coefficient of x that is 5/2 so we get

x² + (5/2)x + 8 + (5/2)² - (5/2)²

From the above expression we get

(x + 5/2)² + 8 - 25/4

(x + 5/2)² + (32 - 25)/4

(x + 5/2)² + 7/4

Thus we have written the expression in the form (x + p)² + q as (x + 5/2)² + 7/4.

Learn more about Quadratic polynomial at:

brainly.com/question/18756459

Answer:

11/5

Step-by-step explanation:

y2-y1/x2-x1

= -3-8/4-9

= -11/-5

= 11/5

Answer:

1/3 and 5/15

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Option D is the only equation where the y-term gets eliminated upon simplifying

11y + 17 = 5y - 10 + 6y

11y + 17 ≠ 11y - 10

We need AC ≅ XZ to show that triangle ABC ≅ triangle XYZ by ASA congruence of triangle.

What is ASA congruence of triangle?

The two triangles are considered to be congruent according to the ASA rule if any two angles and the side located between the angles of one triangle are equal to the corresponding two angles and side located between the angles of the second triangle.

We are given the following:

1. ∠A ≅ ∠X

2. ∠C ≅ ∠Z

Now, in order to show the triangles as congruent by ASA congruence of triangle, we need the side which is in between both the angles.

The sides in between both the angles are AC and XZ.

Hence, we need AC ≅ XZ to show that triangle ABC ≅ triangle XYZ by ASA congruence of triangle.

Learn more about ASA congruence of triangle from the given link

https://brainly.com/question/9513034

#SPJ1

If x = 11.424242…, then 100x = 1142.424242…. So you have

100x - x = 1142.424242… - 11.424242…

99x = 1131

x = 1131/99 = 377/33

Step-by-step explanation:

\(y = \sqrt{ \frac{x + 7}{x - 2} } \\ case1)x = 5 \\ y = \sqrt{ \frac{5 + 7}{5 - 2} } = \sqrt{ \frac{12}{3} } = \sqrt{4} = 2 \\ y = 2 \\ case2) \: y = 4 \\ 4 = \sqrt{ \frac{x + 7}{x - 2} } \\ squaring \: both \: side \\ {4}^{2} = { (\sqrt{ \frac{x + 7}{x - 2} } )}^{2} \\ 16 = \frac{ x + 7}{x - 2} \\ 16(x - 2) = x + 7 \\ 16x - 32 = x + 7 \\ 16x - x = 7 + 32\\ 15x = 39 \\ x = \frac{39}{15} = 2.6\)

Answer:

12a - 18

Step-by-step explanation:

6 x 2 = 12 (then add the "a" = 12a

6 x 3 = 18

put the minus in the middle then get

12a- 18

a) Fiscal policy: Increase government spending or reduce taxes to boost aggregate demand (AD). Monetary policy: Lower interest rates or increase money supply to stimulate AD.

b) Impact depends on SRAS slope. Output ↑, unemployment ↓ in short run. Inflation ↑ if SRAS is steep.

c) Higher inflation expectations from persistent expansionary policies can lead to increased wages and prices, resulting in higher inflation in the long run.

d) Expansionary fiscal policy can lead to budget deficits, crowding out private investment, higher government debt, future tax burdens, and dependency on government intervention.

a) Fiscal policy involves using government spending and taxation to influence aggregate demand (AD) and stabilize the economy. To minimize the unemployment rate, the prime minister could implement expansionary fiscal policy by increasing government spending or reducing taxes. This would lead to an increase in AD, stimulating economic activity, and potentially reducing unemployment. Monetary policy, on the other hand, involves actions taken by the central bank to influence the money supply and interest rates. The prime minister could work with the central bank to implement expansionary monetary policy, such as lowering interest rates or conducting open market operations to increase the money supply. This would encourage borrowing and spending, boosting AD and potentially reducing unemployment.

b) If the central bank helps the prime minister achieve the goal of minimizing the unemployment rate, it can have short-run effects on both the unemployment rate and the inflation rate. Expansionary fiscal and monetary policies can increase AD, leading to increased output and potentially reducing unemployment in the short run. However, the impact on inflation will depend on the slope of the short-run aggregate supply (SRAS) curve. If the SRAS is relatively flat, the increase in output will have a larger impact on reducing unemployment without significantly increasing inflation. Conversely, if the SRAS is steep, the increase in output may lead to a significant increase in inflation with only a modest reduction in unemployment.

c) The opposition leader's argument is related to the long-run implications of the prime minister and central bank's agreement on inflation expectations. According to the AD-AS model, in the long run, the economy will reach the natural rate of unemployment (NRU) where the SRAS curve intersects the long-run aggregate supply (LRAS) curve. If expansionary fiscal and monetary policies are used persistently to reduce the unemployment rate below the NRU, it can create inflationary pressures. This may result in higher inflation expectations among households and businesses, leading to higher wage demands and increased prices.

d) If the prime minister chooses to use fiscal policy to minimize the unemployment rate, the opposition leader argues that it will also be costly in the long run. This is because expansionary fiscal policy, such as increasing government spending or reducing taxes, can lead to budget deficits. Persistent budget deficits can increase government debt and require borrowing, which may lead to higher interest rates and crowding out private investment. Higher government debt can also result in future tax burdens or reduced government spending on other essential areas, impacting long-term economic growth.

To learn more about SRAS slope, click here:

brainly.com/question/28793630

#SPJ1

Given:

A card is selected randomly from a standard deck of 52 cards.

To find:

The probability of each outcome.

a. a king of heart

b. a queen of spades

c. an ace of flower

d. an ace of diamond​

Solution:

In a standard deck of 52 cards.

Total number of cards = 52

13 cards of each suit (heart, diamond, club, spade).

13 cards are Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King.

a. We need to find the probability of getting a king of heart.

Number of king of heart = 1

\(P(\text{a king of heart})=\dfrac{\text{Number of king of heart}}{\text{Total cards}}\)

\(P(\text{a king of heart})=\dfrac{1}{52}\)

b. We need to find the probability of getting a queen of spades.

Number of queen of spades = 1

\(P(\text{a queen of spades})=\dfrac{\text{Number of queen of spades}}{\text{Total cards}}\)

\(P(\text{a queen of spades})=\dfrac{1}{52}\)

c. We need to find the probability of getting an ace of flower (spades).

Number of ace of flower = 1

\(P(\text{an ace of flower})=\dfrac{\text{Number of ace of flower}}{\text{Total cards}}\)

\(P(\text{an ace of flower})=\dfrac{1}{52}\)

d. We need to find the probability of getting an ace of diamond​.

Number of ace of diamond​ = 1

\(P(\text{an ace of diamond​})=\dfrac{\text{Number of ace of diamond​}}{\text{Total cards}}\)

\(P(\text{an ace of diamond​})=\dfrac{1}{52}\)

Therefore, the required probabilities for each parts are:

(a) \(\dfrac{1}{52}\)

(b) \(\dfrac{1}{52}\)

(c) \(\dfrac{1}{52}\)

(d) \(\dfrac{1}{52}\)

The probabilities for each of the given selections are;

A) 1/52

B) 1/52

C) 1/52

D) 1/52

A) Since total number of cards in the deck is 52 and there is only one king of heart, then;

Probability of selecting a king of heart = 1/52

B) Since total number of cards in the deck is 52 and there is only one queen of spades, then;

Probability of selecting a queen of spade = 1/52

C) Since total number of cards in the deck is 52 and there is only one ace of flower, then;

Probability of selecting an ace flower = 1/52

D) Since total number of cards in the deck is 52 and there is only one ace of diamond, then;

Probability of selecting am ace of diamond = 1/52

Read more about Probability at; https://brainly.com/question/25870256

Answer:  A, C, D

(3/20)*20 = 0.15*20 = 3

0.15*20 = 3

(15/100)*20 = 0.15*20 = 3

all expressions lead to the same result of 3

another thing to notice

3/20 = 15/100 = 0.15 = 15%

which are multiple ways to say the same thing just in a different form

\(\sf \bf {\boxed {\mathbb {GIVEN:}}}\)

Radius of the circle "\(r\)" = \(13\)

Value of \(π\) = \(3\)

\(\sf \bf {\boxed {\mathbb {TO\:FIND :}}}\)

The circumference "\(C\)" of the circle.

\(\sf \bf {\boxed {\mathbb {SOLUTION :}}}\)

\(\implies {\blue {\boxed {\boxed {\purple {\sf {C≈78 }}}}}}\)

\(\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}\)

We know that,

\(\sf\pink{Circumference\:of\:a\:circle \:=\:2πr }\)

\( = 2 \times 3 \times 13\)

\( = 6 \times 13\)

\( = 78\)

Therefore, the circumference of the circle is \(78\).

\(\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}\)

Answer:

B: 34, 55

Step-by-step explanation:

To get generation 7, the relatives of generation 5 and 6 were added. (8+13=21). So, to get generation 8, you need to add the relatives of generation 6 and 7. (13+21). Then, to get the ninth generation, you add the relatives of 7 and 8. (21+34. In the Fibonacci sequence you add the previous 2 numbers together to get the next number. I hope I explained this well I really tried my best to explain this.

The result for the given normal random variables are as follows;

a. E(3X + 2Y) = 18

b. V(3X + 2Y) = 77

c. P(3X + 2Y < 18) = 0.5

d. P(3X + 2Y < 28) = 0.8729

Any normally distributed random variable having mean = 0 and standard deviation = 1 is referred to as a standard normal random variable. The letter Z will always be used to represent it.

Now, according to the question;

The given normal random variables are;

E(X) = 2, V(X) = 5, E(Y) = 6, and V(Y) = 8.

Part a.

Consider E(3X + 2Y)

\(\begin{aligned}E(3 X+2 Y) &=3 E(X)+2 E(Y) \\&=(3) (2)+(2)(6 )\\&=18\end{aligned}\)

Part b.

Consider V(3X + 2Y)

\(\begin{aligned}V(3 X+2 Y) &=3^{2} V(X)+2^{2} V(Y) \\&=(9)(5)+(4)(8) \\&=77\end{aligned}\)

Part c.

Consider P(3X + 2Y < 18)

A normal random variable is also linear combination of two independent normal random variables.

\(3 X+2 Y \sim N(18,77)\)

Thus,

\(P(3 X+2 Y < 18)=0.5\)

Part d.

Consider P(3X + 2Y < 28)

\(Z=\frac{(3 X+2 Y-18)}{\sqrt{77}}\)

\(\begin{aligned} P(3X + 2Y < 28)&=P\left(\frac{3 X+2 Y-18}{\sqrt{77}} < \frac{28-18}{\sqrt{77}}\right) \\&=P(Z < 1.14) \\&=0.8729\end{aligned}\)

Therefore, the values for the given normal random variables are found.

To know more about the normal random variables, here

https://brainly.com/question/23836881

#SPJ4

The correct question is-

X and Y are independent, normal random variables with E(X) = 2, V(X) = 5, E(Y) = 6, and V(Y) = 8. Determine the following:

a. E(3X + 2Y)

b. V(3X + 2Y)

c. P(3X + 2Y < 18)

d. P(3X + 2Y < 28)

Answer:

4.8-46c+13x

Step-by-step explanation: