Match the metric units on the left with their
approximate equivalents on the right. Not all the
options on the right will be used.
1 meter
kilogram
1 liter
1 cup
I mile
2
pounds
1 quart
I yard

We know that,

\( \rightarrow \: z = \frac{x - \mu}{\sigma} \\ \)

inserting the given values in the formula

\(\rightarrow \: z = \frac{27.87 - 30}{1.9} \\\rightarrow \: z = - 1.121\)

Area that's left to z = -1.121

Area that's left to -1.121 = 0.1311

= 13.11%

Hence ,

13.11% of the watermelons weigh less than 27.87 pounds

To find the number of watermelons,

We'll find 13.11% of 400

= 13.11% x 400

= 13.11/100 x 400

= 52.44

hence , approx 52 watermelons would be lesser than 27.87 pounds

Answer:

5a²b + 7ab² + 9c + 11a²b - 3ab² - 9c

= (5a²b + 11a²b) + (7ab² - 3ab²) + (9c - 9c)

= 16a²b + 4ab²

The general formula for an exponential function is f(x) = ae^rt while the general form of a quadratic equation is f(x) = ax^2 + bx + c

Thus,

f(x) = 7e^0.5x is an exponential function and

g(x) = 3x^2 + 7x - 4 is a quadratic function

Let us substitute values of x into each function and compare the growth rates

For x = 1,

f(1) = 7e^0.5 = 11.4

g(1) = 3(1)^2 + 7(1) - 4 = 3 + 7 - 4 = 6

For x = 2,

f(1) = 7e^2(0.5) = 19

g(1) = 3(2)^2 + 7(2) - 4 = 12 + 14 - 4 = 22

For x = 3,

f(3) = 7e^3(0.5) = 31

g(1) = 3(3)^2 + 7(3) - 4 = 27 + 21 - 4 = 44

We can see that g(x) is increasing at a faster rate than f(x).

Answer:  It take 6.66 min to complete one lap.

Answer:a b and c are 6

Step-by-step explanation:

The equation of the line is y = 2/3x + 1

The graph represents the given parameter

From the graph, we have the following points that can be used in our computation:

(x, y) = (0, 1) and (3, 3)

The equation of the line is then calculated using the following equation

y = (y₂ - y₁)/(x₂ - x₁) * (x - x₁) + y₁

Where

(x, y) = (0, 1) and (3, 3)

Substitute the known values in the above equation, so, we have the following representation

y = (3 - 1)/(3 - 0) * (x - 0) + 1

Evaluate

y = 2/3 (x - 0) + 1

So, we have

y = 2/3x + 1

Hence, the line equation is y = 2/3x + 1

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If "t" number of years the study started and "y" denote the forest cover area, then the exponential-function representing the relation between "y" and "t" is y = 1500 × \((0.9225)^{t}\).

An "Exponential-Function" is a mathematical expression in which a constant (called the base) is raised to a variable power.

In this case, we want to find an exponential function that relates the area of a forest (y) to the number of years since the start of an environmental study (t).

We know that the forest is decreasing by 7.75% each year, which means that the area of the forest after "t years" will be some percentage of its original area.

The formula for an exponential function is y = a × \(b^{t}\), where "a" = initial value and "b" = growth or decay factor.

In this case, the initial area of the forest is = 1500 km², and

The forest is decreasing by 7.75% each year.

So, the "decay-factor" is = 1 - 0.0775 = 0.9225,

The exponential function that relates the area of the forest (y) to the number of years since the start of the study (t) is:

⇒ y = 1500 × \((0.9225)^{t}\),

Therefore, the required "exponential-function" is y = 1500 × \((0.9225)^{t}\).

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The balance in the account after 13 years is $8233.79.

From the question, we are to use the compound interest formula to compute the balance in the account

From the compound interest formula, we have that

A = P(1 + r/n)^nt

Where A is the amount

P is the principal

r is the interest rate

n is the number of times compounded per year

and t is the time.

From the given information,

P = $7000

r = 3.3%= 0.033

n = 1

t = 13

Putting the parameters into the formula

A = P(1 + r/n)^nt

A = 7000(1 + 0.033/1)^(1×5)

A = 7000(1 + 0.033)^5

A = $8233.79

Hence, the balance is $8233.79

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The number of M&M's that were in the bowl before Amelia arrived is; 12

Let the original amount in the bowl be x. Thus;

If Amelia grabbed 50%, then amount left = (100% - 50%)x = 50%x = 0.5x

Now, we are told that domicick took 50% of what was keft after amelia. Thus; New amount left = 100%x - (0.5x + 0.25x) = 0.25x

Now, we are told that there were finally 3 left after all the deductions. Thus;

0.25x = 3

x = 3/0.25

x = 12

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Step-by-step explanation:

Area of a traingle = 1/2 * base * height

   area = 1/2 * 6 * 4 = 12 cm^2

Answer:

11 and 6

Step-by-step explanation:

Let the two numbers be \(x\) and \(y\).

\(x+y=17, x-y=5 \\ \\ (x+y)+(x-y)=22 \\ \\ 2x=22 \\ \\ x=11 \\ \\ \\ 11+y=17 \implies y=6\)

x= 11;

y= 6.

Say that the names of these two numbers are "x" and "y".

"...their sum is 17", hence:

\(x+y=17\)

"...their difference is 5", hence:

\(x-y=5\)

For this solution, we are going to solve the equation for the first requirement for the "x" variable.

\(x=17-y\)

\((17-y)-y=5\\ \\17-y-y=5\\ \\17-2y=5\\\\-2y=5-17\\ \\-2y=-12\\ \\\frac{-2y}{-2} =\frac{-12}{-2} \\ \\y=6\)

\(x-(6)=5\\ \\x=5+6\\ \\x=11\)

Number x is 11;

number y is 6.

Is the difference between them 5? 11-6=5, correct!

Does their sum equal 17? 11+6= 17, correct!

Hence, 11 and 6 are the numbers for this solution.

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♡ The Question ♡

-Which list accurately sorts the sequence of events that preceded the United States' entry into World War II?

* ୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧

* ♡ The Answer ♡

-The Germans conquered France; the Germans invaded the Soviet Union; Japan attacked Pearl Harbor; the United States declared war on Japan.

*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*

♡ The Explanation/Step-By-Step ♡

-The Germans conquered France and invaded the Soviet Union before the Japanese attacked Pearl Harbor and the United States entered World War II.

*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧

*♡ Tips ♡

-No tips provided!

The Germans conquered France; Japan attacked Pearl Harbor; the Germans invaded the Soviet Union; the United States declared war on Japan and Germany​ is correct list.

A world war is an international conflict which involves all or most of the world's major powers.

The correct sequence of events that preceded the United States' entry into World War II is:

The Germans conquered France; Japan attacked Pearl Harbor; the Germans invaded the Soviet Union; the United States declared war on Japan and Germany.

Therefore, the correct list that accurately sorts the sequence of events is:

The Germans conquered France

Japan attacked Pearl Harbor

The Germans invaded the Soviet Union

The United States declared war on Japan and Germany.

Hence, the Germans conquered France; Japan attacked Pearl Harbor; the Germans invaded the Soviet Union; the United States declared war on Japan and Germany​ is correct list.

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Answer:

The answer is

Step-by-step explanation:

Since the cardboard box is a cube all it's sides are equal

Volume(V) of a cube = l³

where l is the length of one side

From the question

\(V = \frac{125}{8} \: {ft}^{3} \)

The length of each side of the cardboard box is

\( {l}^{3} = \frac{125}{8} \\ \sqrt[3]{ {l}^{3} } = \sqrt[3]{ \frac{125}{8} } \\ l = \frac{5}{2} \)

We have the final answer as

\( \frac{5}{2} \: \: \: feet \\ \)

Hope this helps you

Answer:

5/2 ft

Step-by-step explanation:

The volume of a cube is calculated by the following formula.

Rewrite the formula in terms of the side, as shown.

It is given that the volume of the cardboard box is ft3. Substitute this value into the equation to determine the length of each side of the cardboard box.

Therefore, the length of each side of the cardboard box is 2.5 ft.

Answer:

i hope this helpes

Step-by-step explanation:

a) A group of 16 pays $40 + ($2 x (16 - 10)) = $40 + $6 = $46.

b) The cost function can be represented as C(x) = 40 + 2(x - 10) for x > 10 and C(x) = 40 for x <= 10, where x is the number of people in the group and C(x) is the cost for the group.

c) The domain of the cost function is all non-negative real numbers less than or equal to 50 (0 <= x <= 50), since the maximum group size is 50. The range of the cost function is all non-negative real numbers greater than or equal to 40 (C(x) >= 40), since the minimum charge for a group is $40.

Answer:

a) $52

b) C(x) = 40 + 2x, if x > 10 and x ≤ 50

C(x) = 40, if x ≤ 10

c) Domain = {x ≥ 1 and x ≤ 50}

Range = { from 40 to 140}

The total of yes voter present in the election are 3048.

Now, for the given question;

Let the number of yes voters be 'x'.

Let the number of no voters  be 'y'.

The ratio of yes to no voters is 4:3.

Thus,

x/y = 4/3

or x = 4y/3

Now there are total 5334 voters;

Thus,

x + y = 5334

Put the value of x.

4y/3 + y = 5334

On simplification;

7y = 16002

y = 2286 (no voters)

Now, calculate 'x'.

x = 5334 - 2286

x = 3048 (yes voters)

Thus, the number of yes voters are 3048.

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These are a legitimate probability distribution:

To have a legitimate probability distribution, the probabilities for all possible values of X must satisfy two conditions:

Each probability value must be between 0 and 1, inclusive.

The sum of all probability values must equal 1.

Check if the given probabilities satisfy these conditions:

P(X=-3) = 0.14 (valid)

P(X=1) = 0.1 (valid)

P(X=3) = 0.135 (valid)

P(X=5) = 0.306 (valid)

Now, calculate the remaining probability to check if it satisfies the second condition:

P(X=6) = 1 - (P(X=-3) + P(X=1) + P(X=3) + P(X=5))

P(X=6) = 1 - (0.14 + 0.1 + 0.135 + 0.306)

P(X=6) = 1 - 0.681

P(X=6) = 0.319

Since the calculated probability is valid (between 0 and 1), There is a legitimate probability distribution for the discrete random variable X:

P(X=-3) = 0.14

P(X=1) = 0.1

P(X=3) = 0.135

P(X=5) = 0.306

P(X=6) = 0.319

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Answer:

$42.00

Step-by-step explanation:

We can represent the given information as a ratio:

% of original price : price

                          5% : $2.00

Then, we can multiply both sides of this ratio by 20 (or 100% / 5%) to get 100% of the original price, which IS the original price.

5%      :  $2.00

↓ × 20   ↓ × 20

100%  :  $40.00

Now that we know the original price, we can add $2.00 to get the new price.

$40.00 + $2.00 = $42.00

Answer:

M<E = 62°

Step-by-step explanation:

Since (8x-34)° and (5x+2)° are alternate interior angles, it means they equal each other so...

(8x-34)°= (5x+2)°

if you drop the parenthesis, you get

8x-34= 5x+2

Then you just solve and simplify it

3x= 36 ----> x= 12

Now you know what x is, you would plug it in to either one and you get 62 as your answer meaning m<E is 62°

8(12)-34= 62 (since this angle and angle E are parallel, the angles are the same and that is why if you plug x into this equation, you can find out what the angle of E is)

5(12) +2= 62 ( and since this angle is across from angle E, it means the angles are the same... so that's why if you plugged in x which is 12 into this equation, you can also find E)

I don't know if this helped or not.. it's kind of confusing and hard to explain without being able to show you... sorry.

Answer: 24

Step-by-step explanation: quick brain math

The polynomial -8m²n - 7m²n can be factored using the common factor -m²n. The complete factored form of the polynomial is (-m²n) (8 + 7a).

To find the complete factored form of the polynomial -8m²n - 7m²n, we can factor out common terms from both the terms. The common factor in the terms -8m²n and -7m²n is -m²n. We can write the polynomial as:

-8m²n - 7m²n = (-m²n) (8 + 7a)

Therefore, the complete factored form of the polynomial -8m²n - 7m²n is (-m²n) (8 + 7a). This expression represents the original polynomial in a multiplied form. We can expand this expression using distributive law to verify that it is equivalent to the original polynomial.

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Answer:

slope of fig 1st(m)= 1/4

y-intercept of 1st fig=-1

slope of fig 2= -1

y-intercept of 2nd fig=2

Step-by-step explanation:

Step-by-step explanation:

9 apples for $4.23

Thats the answer

Answer:

\(2xy^2(xy-1)(xy-3)\)

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

Given expression

\(2x^3y^4-8x^2y^3+6xy^2\)

The greatest common factor of all three terms is \(2xy^2\).

Factor this out:

\(2xy^2(x^2y^2-4xy+3)\)

Complete the square:

\(2xy^2(x^2y^2-4xy+4-1)=\)

\(2xy^2((xy-2)^2-1)\)

Factorize further using the identity for the difference of squares:

\(2xy^2(xy-2+1)(xy-2-1)=\)

\(2xy^2(xy-1)(xy-3)\)

On solving the provided question, we can say that first angle is 37.9° . second angle will be 52.1°.

An angle is a fοrm in Euclidean geometry made composed of two rays, called the angle's sides, that meet at a pοint in the middle known as the angle's vertex. In the plane where the rays are placed, twο rays can produce an angle.

An angle is alsο produced when two planes intersect. They're knοwn as dihedral angles. In plane geοmetry, an angle is the form that two rays or lines with a commοn termination might take. The Latin word "angulus," which means "hοrn," is where the English word "angle" comes from. The two rays, also knοwn as the sides of the angle, have a common termination knοwn as the vertex.

x = first angle

Complementary angle is 14.2 degrees more than the cοmplementary angle.

First angle  = x

Second angle = x + 14.2°

Complementary angle

x+x+14.2=90

2x+14.290

2x 90 14.2

2x = 75.8 x = 37.9

First angle is 37.9°.

Second angle will be:

x+14.2°

⇒37.9°+ 14.2°

⇒52.1°

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Answer:  -7x² - 10x + 3

Step-by-step explanation: To find A + B, we need to add the like terms. Combining the terms of A and B, we get: -7x² - 10x + 3. Therefore, the sum of A and B is -7x² - 10x + 3.

Answer: 697

Step-by-step explanation:

17 * 41=

17 * (40+1)=

17 * 40 + 17 * 1=

17 * 10 * 4 + 17=

170 * 4 + 17=

680+17=697

Answer:

$2.85 per person

Step-by-step explanation:

$191.10 * 0.15 = $28.665 tip

total tip divide by 10 people

$28.665/10 = $2.85

Each person has to contribute $2.85 amount for the tip.

Given,

Total no. of person go out for dinner = carrie + her nine friends

                                                             = 1+9 = 10

Amount of the bill is = $191.10

Amount of tip is = 15% of the bill

                           = \(\frac{15 }{100}\) × $  191.10

                           = 28.665

Total amount each person contribute an equal amount for tip is = \(\frac{28.665}{10}\)

=$ 2.85

Each person contribute $2.85 amount for the tip.

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Answer:

B.

Step-by-step explanation:

Since two diameters are intersecting eachother, the angles inside them would be vertical angles so they'll be congruent.

So

m<LYM = m<JYM

Also their arcs would be equal to their angles measures so,

Arc JK = 52°

Answer:

take a look at the explanation

-u divided by h