What can use the distributive property to the algebraic expression 5(x - 7)

987.6 million written in scientific notation is 9.876 × [tex]10^{8}[/tex]

What is scientific notation?

Scientific notation is basically a shortcut for writing numbers. It is a method of expressing real numbers in terms of a significand, multiplied by a power of 10.

When using scientific notation, you're allowed to simplify all the zeros that you have in the number by writing the number as a product of a number and a power of 10. 987.6 million in exponential form is [tex]a^{b}[/tex], a is the base, and b is called the exponent . The term [tex]a^{b}[/tex] is called the exponential expression. 987.6 million = 9.876 x 100,000,000 = 9.876 ×[tex]10^{8}[/tex].

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Answer:

b = [tex]\sqrt{2p/a}[/tex]

Step-by-step explanation:

The given equation is:

p=1/2ab^2

Multiply by 2 on both sides

2p = ab^2

Then divide by a on both sides,

b^2 = 2p/a

take square root on both sides, then we can get subject of b,

b = [tex]\sqrt{2p/a}[/tex]

Hence, the subject of the given equation make the value of b is b = [tex]\sqrt{2p/a}[/tex]

The subject of an equation is the value that is being solved for. An equation is a mathematical statement consisting of an equality sign (=) between two expressions that have the same value. The expression on the left side of the equality sign is called the left-hand side, while the expression on the right side of the equality sign is called the right-hand side. The left-hand side of the equation can be thought of as what is being solved for, while the right-hand side of the equation can be thought of as the clues or tools that are used to solve for the left-hand side. For example, in the equation 3x + 1 = 7, the subject of the equation is the variable x, which is the value that is being solved for.

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The volume of the triangular prism is 308 in³

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

Given that, Alfred made a container shaped like a triangular prism,

Given are the dimensions, 14 in., 4 in. and 11 in.

Volume of a triangular prism = BxHxL/2

= 14x4x11/2 = 616/2 = 308 in³

Hence, The volume of the triangular prism is 308 in³

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Answer:

Here is answer

Step-by-step explanation:

To find the least common multiple (LCM) of three polynomials, we need to find the smallest polynomial that is divisible by all three of them.

Let's start by factoring each of the given polynomials:

ax² - (a² + ab)x+ a²b = a(x - b)x

bx² - (b² + bc)x+ b²c = b(x - c)x

cx² - (c² + ac)x + c²a = c(x - a)x

The LCM of these three polynomials is the smallest polynomial that is divisible by all three of them. In this case, the smallest such polynomial is (x - a)(x - b)(x - c)x. This is because it is divisible by each of the given polynomials and no smaller polynomial is divisible by all three of them.

Therefore, the LCM of the given polynomials is (x - a)(x - b)(x - c)x.

We can conclude that the mayor's plan for annexation is likely to be supported by the town's residents.

What do you mean by  Annexation?

International law defines annexation as the forcible acquisition of one state's territory by another state, typically after the possession of the region by an occupying military force. In most cases, it is considered to be unlawful.

According to the question,

We have the given data:

A political study took a sample of 1,600 voters in the town and found that 69% of the residents favored annexation.

The conclusion of the hypothesis test is that we reject the null hypothesis that the percentage of residents who favor annexation is 65% or lower. The sample data suggests that 69% of residents favor annexation and the p-value associated with the test statistic is 0.07, which is less than the significance level of 0.05.

This indicates that the data is significantly different from the null hypothesis and that the true percentage of residents who favor annexation is likely greater than 65%.

Therefore, we can conclude that the mayor's plan for annexation is likely to be supported by the town's residents.

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Answer:

a. -4

b. 1/4

Step-by-step explanation:

a. [tex]\textrm{slope}_{||} = \dfrac{\textrm{rise}}{\textrm{run}} = \dfrac{-4}{1} = -4[/tex]

b. [tex]\textrm{slope}_\perp = \dfrac{-1}{\textrm{slope}_{||}} = \dfrac{-1}{-4} = \dfrac{1}{4}[/tex]

It is true that qualitative variable categories must be mutually exclusive and exhaustive as a whole.

It has been observed that when two occurrences are mutually exclusive, they cannot take place simultaneously. However, it need not entail that one of the two occurrences must take place. As a result, when two events are exhaustive of one another, one of them is said to occur.

It signifies that two occurrences cannot happen at the same moment if they are mutually exclusive. However, it doesn't entail that one of the two events must take place. If two occurrences are mutually exclusive, then one of them must take place.

The categories (answer possibilities) must, in the first place, be mutually exclusive, which means they cannot overlap. In order to give all alternatives that might make up a response list, survey answer options must be collectively thorough.

For instance, the act of flipping a coin is said to be both mutually exclusive and collectively exhaustive. Either heads or tails must result in this situation. These are variables, then.

Therefore,

It is true that qualitative variable categories must be mutually exclusive and exhaustive as a whole.  

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Answer:

j = - 8

Step-by-step explanation:

1 - j/4 - 3

1 is also 4/4

so

4/4 - j/4 = 3

4 - j/ 4= 3

multiply by 4 on both sides

which gets you

-j  + 4 = 12

minus 4 from both sides

-j = 8

j = -8

Answer:j=-8 I hope this helps

Step-by-step explanation:

1-j/4=3

Multiply both sides of the equation by 4

which gives you

4-j=12

Move the constant to the right-hand side and change its sign
-j=12-4

Subtract the numbers

-j=8

Change the signs on both sides of the equation

j=-8 - This is your answer

Answer:

50x + 9500 ≤ 27500

x ≤ 360

Step-by-step explanation:

50x + 9500 ≤ 27500  Subtract 9500 from both sides

50x + 9500 - 9500 ≤ 27500 - 9500

50x ≤ 18000  Divide both sides by 50

[tex]\frac{50x}{50}[/tex] ≤ [tex]\frac{18000}{50}[/tex]

x ≤ 360

We can arrange the group in 120960 different ways.

Given,

Number of adults = 7

Number of children = 4

We have to find the number of ways they can stand when no two children are allowed to stand together;

Here,

Arrange 7 adults in a row of 7 ; 7

Number of arrangements = 7! = 5040

Consider that there are four possible placements for a child, but only one youngster can be placed in each of them: on either side of the row of adults, or in between two adults.

Consequently, pick one place for each youngster from the possibilities below: 4 for the first adult, 3 for the second,... the final adult's two options are = 4 × 3 × 2 = 24 arrangements

Add the two groupings together =  5040 × 24 = 120960

Therefore,

There is 120960 ways to arrange the standing position of the group.

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Answer:

Step-by-step explanation:

g(x) = (-x)1/2

453 cubic units of food is poured to the cylindrical dog feeder of 18 inches tall and has a diameter of 8 inches.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Given that the cylindrical dog feeder is 18 inches tall and  has a diameter of 8 inches

height is 18 inches

Diameter=8 inches

Radius =4 inches

The feeder is currently half full, how much more food can be poured into the feeder.

We know that volume of a cylinder is V=πr²h

Substitute the values of r and h in the given formula.

V=22/7(4)²×18

=22×16×18/7

=6336/7

=905.142.

As the feeder is currently half full, so let divide the volume by 2.

905.142/2

=452.5

=453

Hence, 453 cubic units more food is need or poured into the feeder.

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Answer:

SSS, SAS, ASA, AAS

Step-by-step explanation:

s = sides

a = angle

The system of inequalities that matches the graph is defined as follows:

The first solid line has a positive slope and goes through (-1, -3) and (0, 0). Everything to the left of the line is shaded, hence this is the upper bound of the interval, as it is a solid line, it is a closed interval.

This line has an intercept of zero and a slope of 3, as when x increases by one, y increased by 3, hence the constraint is defined as follows:

y ≤ 3x

he second dashed line has a negative slope and goes through (-2, 3) and (1, -3). Everything to the right of the line is shaded, meaning that this is the lower bound of the interval, with an open interval.

When x increased by 3, y decayed by 6, hence the slope of the line is of:

m = -6/3 = -2.

Then:

y = -2x + b.

When x = 1, y = -3, then the intercept is given as follows:

-3 = -2 + b

b = -1.

Thus the constraint is of:

y > –2x – 1.

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Answer:0.41

Step-by-step explanation:

The required probability of getting exactly 3 heads is 0.3.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

here,
Total sample space = 2×5 = 10
Favorable outcome (3 heads) = 3
Probability is given of getting exactly 3 heads
= favorable outcome / total sample space

Substitute the value in the above equation
= 3 / 10
= 0.3

Thus, getting the 3 heads while tossing a coin 5 times has a probability of 0.3.

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The equation y = mx + b, when isolated for the variable m, gives us m in terms of x, y, and b, as m = (y - b)/x.

What is the isolation of a variable in an equation?

Equations are relations between two quantities involving variables raised to multiple powers, making up terms along with numerals.

Isolation is the process of moving one variable to one-side of the equation and everything else on the other side of the equation.

How to solve the question?

In the question, we are given an equation, y = mx + b, and are asked to write m in terms of x, y, and b.

This means that we need to isolate the variable m, to get an expression equal to m.

The isolation of the variable m can be done as follows:

y = mx + b,

or, y - mx = mx + b - mx {Subtracting mx from both sides},

or, y - mx = b {Simplifying},

or, y - mx - y = b - y {Subtracting y from both sides},

or, -mx = b - y {Simplifying},

or, (-mx)/(-x) = (b - y)/(-x) {Dividing both sides by (-x)}

or, m = (y - b)/x {Simplifying}.

Thus, the equation y = mx + b, when isolated for the variable m, gives us m in terms of x, y, and b, as m = (y - b)/x.

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The equation y = mx + b, when isolated for the variable m, gives us m in terms of x, y, and b, as m = (y - b)/x.

What is the isolation of a variable in an equation?

Equations are relations between two quantities involving variables raised to multiple powers, making up terms along with numerals.

Isolation is the process of moving one variable to one-side of the equation and everything else on the other side of the equation.

How to solve the question?

In the question, we are given an equation, y = mx + b, and are asked to write m in terms of x, y, and b.

This means that we need to isolate the variable m, to get an expression equal to m.

The isolation of the variable m can be done as follows:

y = mx + b,

or, y - mx = mx + b - mx {Subtracting mx from both sides},

or, y - mx = b {Simplifying},

or, y - mx - y = b - y {Subtracting y from both sides},

or, -mx = b - y {Simplifying},

or, (-mx)/(-x) = (b - y)/(-x) {Dividing both sides by (-x)}

or, m = (y - b)/x {Simplifying}.

Thus, the equation y = mx + b, when isolated for the variable m, gives us m in terms of x, y, and b, as m = (y - b)/x.

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The mark that is required to receive an A on the test is; 75.68

The formula for z-score here with the parameters given is;

z = (x' - μ)/σ

where;

x' is sample mean

μ is population mean

σ is standard deviation

We are given;

p-value = 10% = 0.1

μ = 68

σ = 6

Now, from z-score tables, the z-score at a p-value of 0.1 is z = 1.28. Thus;

1.28 = (x' - 68)/6

x' = 68 + (1.28 * 6)

x' = 75.68

We conclude that this value is the mark required to receive an A on the test.

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Answer:

-48y+24

Step-by-step explanation:

−6⁢(⁠4y + 4y + (−4)⁠)

=-6(8y+-4)

=-48y+24

Answer:

-48y + 24

Step-by-step explanation:

−6⁢(⁠4y + 4y + (−4)⁠) =

= −6⁢(⁠8y - 4)

= -48y + 24

Answer:

Step-by-step explanation:

7/8
------
3/10

use the fraction rule: 7x10/8x3- 35/12

try that, im not sure if its fully correct

Answer:

Below

Step-by-step explanation:

3x+15      <==== factor out '3'

3 * ( x+5)       done !

The value of x for the given figure is 2.35 if triangle ΔCDG~ ΔEDF

Three edges and three vertices define a triangle as a polygon. One of geometry's fundamental shapes is this one. The designation "triangle ABC" refers to a triangle containing the vertices A, B, and C. When three points are non-collinear in Euclidean geometry, they each produce a distinct triangle and plane. Since it was first described on the first page of Euclid's Elements, the vocabulary for classifying triangles is more than two thousand years old. Modern categorization names are either literal transliterations of Euclid's Greek or their Latin interpretations.

A closed triangle has 3 sides, 3 angles, and 3 vertices. It is a 2-dimensional shape. Polygons include triangles as well. ABC is used to signify a triangle in the previous illustration.

FD/DC=ED/DG

2x+7/48=5x-2/40

40(2x+7)=48(5x-2)

80x+280=240x-96

160x=376

x=2.35

Therefore, The value of x for the given figure is 2.35 if triangle ΔCDG~ ΔEDF

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Answer:

x = 3[tex]\sqrt{7- x}[/tex]

Step-by-step explanation:

so what you do here is move the x to the other side.

X^2 = 63 - x

then you square root both sides

so [tex]\sqrt{x^{2} }[/tex] and [tex]\sqrt{63 - x}[/tex]

so you end up with

x =   [tex]\sqrt{63 - x}[/tex]

so now we ask what can we take out? 9 times 7 is 63 and 9 is a perfect square so when we take the square root of that, we end up with

x = 3[tex]\sqrt{7- x}[/tex]

have a good day :)

Retain the null because 1.74 is greater than 1.645.

What is z - test statistic?

Any statistical test for which the test statistic's distribution under the null hypothesis can be roughly represented by a normal distribution is known as a Z-test.

Z-tests examine a distribution's mean.

Let X be the average time that prescholars spend on tablets.

X ~ N(μ, α^2)

To test H0: μ = 3 hours Vs H1: μ ≠ 3 hours.

The z - test statistic is obtained as 1.74.

Taking level of significance α = 0.05

Zα/2 = [tex]Z_0_._0_2_5 = 1.96[/tex]

Since the observed z - statistic is 1.74 which is less than Zα/2 = [tex]Z_0_._0_2_5 = 1.96[/tex],

so we retain the null hypothesis.

Hence, retain the null because 1.74 is greater than 1.645.

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Complete question:

Complete question is attached below.

Answer: B

Step-by-step explanation:

A - Nope.

B - Possibility.

C. Nope. (2.23606797)

D. Nope.

When facing questions like this, it can be easier to use the process of elimination.

Answer:

3y, 9y²

Step-by-step explanation:

We use laws of binomial

(a+b)²=a²+2ab+b²

From this, we get

15x × * × 2 = 90xy

2×*=6y

*=3y

Now, we square this term to get the last term

3y×3y=9y²