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Given:

Given that four far dice are thrown.

Required: Probability of getting an even number on each one.

Explanation:

The sample space is

The number of elements in the sample space is

Let E be the event of getting even on each dice. Then

The number of elements in E is

The probability of getting even on each dice is

The second option is correct.

Final Answer: The probability of getting even on each dice is 1/16.

Answer:

She can run 3/5 miles in 1 hour

Explanation:

Given that Ava can run 4/5 of a mile in 4/3 of an hour, we want to find how far she can run in 1 hour.

Let x represent the number of miles she can run in one hour.

The statement can be represented in the pair of equations:

Using these equations, we have:

That is, she can run 3/5 miles in 1 hour

Answer:

x=7, DF = 174

Step-by-step explanation:

18x-39=9x+24

9x=63

x=7

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Given:

The expression given is,

Required:

To find the coefficient of the third term.

Explanation:

Let us expand the expression to find the coefficient.

Hence, the coefficient of the third term is 40.

Final Answer:

The coefficient of the third term is 40.

Option A is correct.

The answers of the given questions are:

Given: There are 6 teaspoons of garlic powder and 15 teaspoons of salt in a triple batch of spice mix.

Let x be the teaspoons of salt.

Salt used with 8 teaspoons of garlic powder:

6/15 = 8/x

x = 20

Therefore, 20 teaspoons of salt is used with 8 teaspoons of garlic powder.

6 + 15 = 21 teaspoons of  spice mix

Salt used in 14 teaspoons of spice mix:

21/15 = 14/x

x = 10 teaspoons of salt.

Therefore, if there are 14 teaspoons of spice mix, 10 teaspoons of salt is there in it.

If 6 teaspoons of garlic powder are used then,

21-6 = 15 teaspoons of more salt is used

Therefore, 15 teaspoons of more salt is there than garlic powder if 6 teaspoons of garlic powder are used.

The answers of the given questions are:

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Answer:

Step-by-step explanation:

Soh Cah Toa

S stand for sine, C stand for Cosine and the T stand for Tangent

'o' is the opposite, 'a' stand for adjacent (next to) and h stand for hypotenuse (the longest length of the triangle)

[tex]sin(\theta)=\frac{opposite}{hypotenuse}[/tex]

[tex]cos(\theta)=\frac{adjacent}{hypotenuse}[/tex]

[tex]tan(\theta)=\frac{opposite}{adjacent}[/tex]

We care about angle A and we want sine. So we will use the first equation.

The opposite from A is 3 and the hypotenuse is 5.

[tex]sin(A)=\frac{3}{5}[/tex]

A set of data has a mean of 9.6 and a standard deviation of 0.8. The number in the data set that would have a z-score of -1.5 is

x =8.4

This is further explained below.

The number of normal deviations within which the value of a raw score is either above or below the average value of what is observed or measured is the number that is referred to as the standard score in the field of statistics.

Raw scores that are greater than the mean are assigned positive standard scores, and raw scores that are equal to or lower than the mean are assigned negative standard scores.

Generally, the parameters of the solutionare

[tex]\mu &=9.6 \quad \sigma=0.8 \quad z=-1.5 \\\\z &=\frac{x-\mu}{\sigma} \\\\-1.5 &=\frac{x-9.6}{0.8} \\[/tex]

Where

z=distribution

x=mean

[tex]\sigma[/tex]=standard deviation

u=population mean

Hence, solve for x

x =-1.2+9.6

x =8.4

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The given system of equations : 6x - y = 2 and 4x - y = -8.

6x - y = 2 ( 1 )

4x - y = -8 ( 2 )

for the value of y, use substitution method:

Solve the equation (1) for y :

6x - y = 2

y = 6x - 2

Susbtitute the value of y in the equation ( 2 )

4x - y = - 8

4x - (6x - 2) = - 8

4x - 6x + 2 = - 8

4x -6x = - 8 - 2

-2x = -10

Divide both side by ( -2)

-2x/(-2) = -10/(-2)

x = 5

Substitute x = 5 in the equation ( 1 )

6x - y = 2

6( 5 ) - y = 2

30 - y = 2

y = 30 - 2

y = 28

So, the value of y is 28

Answer : y = 28

According to the given data we have the following:

19 employees that earn $360

18 employees that earn $400

8 employyes that earn $480

5 employees that earn $600

The total employees would be=19+18+8+5=50

Therefore, to find the average we have to put at the numerator the amount of wages times of what correspond to each employee, and at the denominator the total of employees which are 50. Therefore, the expression that represents the average wages the company pays per employee each week would be 2.

The midpoint of the segment with the following endpoints, (4, 2) and
(7, 6) is (5.5, 4).

How to determine the midpoint of a given segment?
The center point of a straight line can be located using the midpoint formula. We can use this midpoint formula to determine the coordinates of the supplied line's midpoint in order to discover its location on a graph. Assuming that the line's endpoints are (x₁, y₁) and (x₂, y₂), the midpoint (a, b) is determined using the following formula:
(a , b) ≡ (((x₁ + x₂)/2), ((y₁ + y₂)/2))

Let the line segment be AB having endpoints as A(4, 2) and B(7, 6);
also let the co-ordinates of midpoint be C = (a, b)
Using the given formula in the available literature,
(a, b) = ((4 + 7)/2, (2 + 6)/2)
Equating parts of the previous equation, we get,
a = (4 + 7)/2 = 11/2 = 5.5
b = (2 + 6)/2 = 4
Thus, the midpoint of the segment is (5.5, 4).

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Solution

We have the following info given:

x: 75,76, 91, 65,48,75,85,62,51,80,94,43

y: 69, 88, 101, 63, 59, 82, 86, 67, 56, 84, 105, 44

After apply OLS (Ordinary LEast Squares) we got the following regression line:

y= 1.0607x + 0.6442

We want to find the best prediction for a student who scored 52 in the first test so we have this:

y= 1.0607* 52 + 0.6442 = 55.80

Then the best prediction for this case is 55.80

Lengths of similar triangles and similar polygons are proportional to each other so, answer to the question in image are-

a. ZY=20

b. X=20.8

c. 9miles

What are similar polygons?

similar polygons are the polygons in which all the corresponding angles are same. Hence, they have same shape. The ratio of sides in any two similar polygons are same. This concept of constant ratio of sides is useful in evaluating the length of sides.

a.    A/a=B/b=C/c = D/d

       WX/HI=ZY/JK

   ZY=20

b.  X=(2.4×39)/4.5

                  X= 20.8

c. If 5cm represents 2miles it implies 1cm represents

1cm=2/5

So, 22.5cm will represent

22.5cm=2/5×22.5

22.5cm=9miles

This means that 22.5cm track represents the distance of 9 miles on map

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Using Venn probabilities, there is a 0.77 = 77% probability that a randomly chosen contestant tried tapping the ground or charmed 5-10 worms.

In a Venn probability, two non-independent events are related with each other, as are their probabilities.

The "or probability" is given according to the following rule:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

In the context of this problem, the events are given as follows:

From the text, the probabilities of the events are given as follows:

P(A) = 0.22, P(B) = 0.71, P(A and B) = 0.16.

Hence the or probability is given replacing the values as follows:

P(A or B) = P(A) + P(B) - P(A and B) = 0.22 + 0.71 - 0.16 = 0.77.

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Given:

The length of the marathon is L= 46,145 yards.

The length covered by terrence is d = 23,561 yrads.

The objective is to find the remaining distance need to cover by terrence.

To calculate the remaining distance, we will use the relation,

On plugging the values in the above relation, we get,

Hence, Terrence needs to run about 23000 yards.

The solution to the given inequality would be n ≤ 1/35 which is the correct answer would be an option (C).

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

We have to determine the solution of the inequality n minus three-fifths is less than or equal to negative four sevenths for n.

As per the given condition, translate the phrase into an algebraic inequality as :

⇒ n - 3/5 ≤ - (4/7)

⇒ n ≤ 3/5 - (4/7)

⇒ n ≤ (21 - 20)/35

⇒ n ≤ 1/35

Therefore, the solution to the given inequality would be n ≤ 1/35.

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Answer: She needs approximately 142.5 pounds

Explanation:

From the information given,

A pound of fertilizer covers 39 square feet of lawn.

If the lawn measures 5557.4 square feet, then

the number of pounds of fertilizer that she needs to buy = 5557.4/39 = 142.4975

Rounding to the nearest tenth,

She needs approximately 142.5 pounds

From the question we were given the following:

Area of the square is 19 square units

Area of the circle is 30 square units

Area of intersection is 3 square units.

We are asked to find the area in square units of the entire coloured region.

So,

Are of Square = 19 square units

Are of Circle = 30 square units

Area of Intersection = 3 square units

Area of coloured region = Area of Square + Area of Circle - Area of Intersection

Therefore, Area of coloured region = 19 + 30 - 3

= 46 saqure units.

In order to solve this problem, first let's draw the corresponding image to the problem:

Then, to calculate the distance x, we can use the sine relation of the angle of 18°.

The sine relation is the length of the opposite side to the angle over the length of the hypotenuse.

So we have:

So the distance wanted is 7.42 ft.

First, let's find the measure of the third side, using the law of cosine:

Now, let's use Heron's formula to calculate the area:

We have the function:

And we have to find the inverse function.

We can write this as:

We can solve this as:

The inverse function is:

The domain of H is all the real numbers, as the domain of H^-1.

Based on the fact that the submarine's depth was descended to at a constant rate, the submarine's depth relative to sea level with the passing of the first minute was -6⁴/₅ miles

The submarine descended at a constant rate to the current depth of -34 miles in 5 minutes. This means that the rate can be found by the formula:
= Current depth / Time

= -34 / 5

= -6.8 miles per minute

After the first minute, the depth is:

= -6.8 x 1

= -6.8 miles

This number in fractions is:

= -6 + 8/10

= -6 + 4 / 5

= -6⁴/₅ miles

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Let's begin by listing out the information given to us:

To know which is greater between 0.123 To know which i3& 0.68, let's express it in tenth, hundredth & thousandth

0.123 has 3 decimal places, which means it is 123/1000

0.68 has 2 decimal places, which means it is 68/100

When you multiply by 100, we have:

0.123 * 100 = 12.3

0.68 * 100 = 68

It becomes very evident that 0.68 is greater than 0.123

Supplementary angles add 180 degrees.

One of the two angles is 8 degrees more than 3 times the other.

If one of the angles is A and the other is B, then:

As they are supplementary, they add 180 degrees:

We replace the information of the second equation in the first one and solve:

Now we can solve for the other angle:

The measure of the angles is 34.4 degrees and 111.2 degrees.

Answer:

Step-by-step explanation:

Number of yellow marbles =13

Number of teal marbles  = 13

Two marbles are drawn randomly

Probability that both marbles are teal

Hence the probability that both marbles are teal is 0.026

The raisins cost $3.00 a box while the nuts cost $6.00 a tin.

The graph in the picture provide to us, in the shaded region, the relation between the number of boxes of raisins and the tins of nuts that can be buyed without spend more than $12.00.

We can check in the graph that the point representing a mixture consisting of 3 boxes of raisins and 1 tin of nuts is out of the shaded region.

Therefore, Randy can't make this mixture without spend no more than $12.00

Te solutions to the linear equation given as y = 12x + 24 are (0, 24), (1, 36) and (2, 48)

From the question, the linear equation is given as

y = 12x + 24

To determine the solutions, we assume values for the variable x and then calculate the y values

Having said that, we have

y = 12x + 24

Set x = 0

So, we have

y = 12 x 0 + 24 = 24

Set x = 1

So, we have

y = 12 x 1 + 24 = 36

Set x = 2

So, we have

y = 12 x 2 + 24 = 48

So, the ordered pairs of the solutions are (0, 24), (1, 36) and (2, 48)

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All of the triangles are an isosceles triangle, which means that they have two congruent side, and two congruent angles.

The first triangle has ∠B as 56°, AB ≅ BC.

The angle opposite to AB and BC are therefore, congruent, which means that

∠A + ∠B +∠C = 180°

∠A + 56° + ∠A= 180° (∠A and ∠C are congruent)

2∠A = 180° - 56°

2∠A = 124

∠A = 62°

The second triangle has ∠C equal to 62°. Since ∠A and ∠Care the angle opposite to the congruent side, they are also congruent which means ∠A = 62°.

The fourth triangle which has an exterior angle of ∠C equal to 118° forms a linear pair, and are thus supplementary

∠C = 62°, and both ∠C and ∠A are the corresponding angles to the congruent sides, it follows that they are also congruent.

∠A = 62°.

Conclusion

The following triangles have m∠A = 62°, first, second, and fourth triangle.

To create the abbreviated expression, combine similar terms by adding them all together. If the expression be [tex]$\sqrt{112 x^{10} y^{13}}$[/tex] then expression exists [tex]$4 \sqrt{7} x^5 y^6 \sqrt{y}$[/tex].

Solving a math problem is the same thing as simplifying an expression. You basically strive to write an expression as simply as you can when you simplify it. In the conclusion, there shouldn't be any more multiplying, dividing, adding, or removing to do.

Start by recognizing the like terms, or terms with the same variables and exponents, in algebraic formulas. Then, to create the abbreviated expression, combine similar terms by adding them all together.

Let the expression be [tex]$\sqrt{112 x^{10} y^{13}}$[/tex]

separating the roots of the expression, we get

[tex]$\sqrt{112 x^{10} y^{13}}=\sqrt{112} \sqrt{x^{10}} \sqrt{y^{13}}$[/tex]

simplifying the above equation, we get

[tex]$=\sqrt{112} \sqrt{x^{10}} \sqrt{y^{13}}$[/tex]

Simplify [tex]$\sqrt{x^{10}}= x^5$[/tex]

[tex]$=\sqrt{112} x^5 \sqrt{y^{13}}$[/tex]

Simplify [tex]$\sqrt{y^{13}}=y^6 \sqrt{y}$[/tex]

[tex]$=\sqrt{112} x^5 y^6 \sqrt{y}$[/tex]

[tex]$=\sqrt{112}=4 \sqrt{7}$[/tex]

[tex]$=4 \sqrt{7} x^5 y^6 \sqrt{y}$[/tex]

Therefore, the correct answer is [tex]$4 \sqrt{7} x^5 y^6 \sqrt{y}$[/tex].

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[tex] \sqrt{25} [/tex] ()

what's the square root ​?

√25 = 5

because 5*5= 25

________________________

Answer

√25 = 5