Solve The Compound Inequality By Identifying Which Two Inequalities Will Be Used To Graph The Solution. (2024)

Let us take each expression one by one.

1.

[tex](-14+\frac{3}{2}b)-(1+\frac{8}{2}b)[/tex]

On solving,

[tex]undefined[/tex]

2.

[tex]undefined[/tex]

SOLUTION:

Case: Right-angle triangle

Given: A right-angle triangle

Required: Find the cosine of angle F

Method:

[tex]\begin{gathered} \cos\theta=\frac{Adj}{Hyp} \\ \cos\theta=\frac{13}{85} \\ \cos\theta=0.153 \end{gathered}[/tex]

Final answer:

0.153

z-score is calculated as follows:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

where x is the raw score, μ is the mean, and σ is the standard deviation.

Substituting with x = 71 in, μ = 69.6 in, and σ = 3.05 in, we get:

[tex]z=\frac{71-69.6}{3.05}=\frac{1.4}{3.05}=0.46[/tex]

We want to know the probability of z greater than 0.46. We can do this with the help of the next table:

(Notice that the table shows the probability of z less than some z-score)

P(Z > 0.46) = 1 - P(Z < 0.46) = 1 - 0.6772 = 0.3228

Let's recall what is the order of operations.

1. Do things in Parentheses First

2. Calculate Exponents, Powers and Roots

3. Multiply and divide

4. Finally, you can add or subtract.

For not forgetting the specific order, you should remember the acronym PEMDAS, as follows:

• Parentheses

,

• Exponents

,

• MD Multiply and divide

,

• AS Add and subtract.

The letters in the word MATHEMATICS make up the universal set.

The Universal Set is written out to be:

[tex]U=\mleft\lbrace M,A,T,H,E,I,C,S\mright\rbrace[/tex]

Note that we do not need to repeat letters when listing out the elements of the set.

The letters can either be vowels or consonants.

If E is the set of vowels appearing in the Universal set, we have the set to be:

[tex]E=\mleft\lbrace A,E,I\mright\rbrace[/tex]

The FIRST OPTION is correct.

The given expression is

[tex](x-\frac{1}{x})^3[/tex]

According to Pascal's Triangle, the third row is 1 3 3 1.

This means the binomial expansions must have 4 terms, where each number belongs to each of them as a coefficient.

Now, the binomial expansion would be

[tex](x-\frac{1}{x})^3=x^3+3x^2(-\frac{1}{x})+3x(-\frac{1}{x})^2+(-\frac{1}{x})^3[/tex]

Now, we need to solve each parenthesis using the distributive property.

[tex]x^3-\frac{3x^2}{x}+\frac{3x}{x^2}-\frac{1}{x^3}[/tex]

Then, we simplify variables, remember that division of powers is solved by subtracting exponents

[tex]x^3-3x^{2-1}+3x^{1-2}-\frac{1}{x^3}=x^3-3x+3x^{-1}-\frac{1}{x^3}[/tex]

At last, we place the negative power as denominator

[tex]x^3-3x+\frac{3}{x}-\frac{1}{x^3}[/tex]

Consider that the sum of the length of the segments DE and EF is equal to the length of the segment DF. Then, by using the given expression for each segment, you can write:

(3x - 1) + (13) = 6x

Solve the previoud equation as follow:

(3x - 1) + (13) = 6x cancel out parentheses

3x - 1 + 13 = 6x simplify like terms left side

3x + 12 = 6x subtract 6x both sides and 12 both sides

3x - 6x = - 12 simplify left side

-3x = -12 divide by -3 both sides

x = -12/(-3)

x = 4

Hence, the value of x is x = 4

The first step to solve the problem is to graph the equation:

[tex]f(x)=2x^2+2x-24[/tex]

To create the graph we need to create a table with a few ordered pairs. We will use the values of x going from 0 to 10 in increments of 1.

We have:

[tex]\begin{gathered} f(0)=2\cdot0^2+2\cdot0-24=-24 \\ f(1)=2\cdot1^2+2\cdot1-24=-20 \\ f(2)=2\cdot2^2+2\cdot2-24=-12 \\ f(3)=2\cdot3^2+2\cdot3-24=0 \\ f(4)=2\cdot4^2+2\cdot4-24=16 \\ f(5)=2\cdot5^2+2\cdot5-24=36 \\ f(6)=2\cdot6^2+2\cdot6-24=60 \\ f(7)=2\cdot7^2+2\cdot7-24=88 \\ f(8)=2\cdot8^2+2\cdot8-24=120 \\ f(9)=2\cdot9^2+2\cdot9-24=156 \\ f(10)=2\cdot10^2+2\cdot10-24=196 \end{gathered}[/tex]

We calculated the points now we need to graph the function.

The zeros of the function are the points at which it crosses the "x" axis. This functtion crosses the axis at he points "-4" and "3".

the triangle are congruent by ASA

[tex]\begin{gathered} \angle DBC\cong\angle ABD \\ BD\cong BD \\ \angle BDC\cong BDA \end{gathered}[/tex]

ANSWER

[tex]72.5\operatorname{\%}[/tex]

EXPLANATION

To find the efficiency of the transmission and drive mechanism, we have to divide the output power by the input power and multiply by 100.

That is:

[tex]\begin{gathered} \frac{174}{240}*100 \\ 72.5\% \end{gathered}[/tex]

That is the answer.

You have the following expression:

2|-3x| + 1

In order to find the value of the previous expression when x = 7, consider that bars |-3x| means absolute value of -3x. The result of an absolute value is always a positive number, indeendently of the sign of the quantity inside the absolute value.

Then, when you replace x= 7, you obtain:

2|-3(7)| + 1 =

2|-21| + 1 =

2(21) + 1 =

42 + 1 =

43

Hence, the result is 43

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Define a random a bias sample

Sampling bias occurs when some members of a population are systematically more likely to be selected in a sample than others. A random sample is a sample that is chosen randomly. It could be more accurately called a randomly chosen sample. Random samples are used to avoid bias and other unwanted effects.

STEP 2: Answer Question A

Survey Method 2 is a random sample since the names are chosen without looking

STEP 3: Answer Question B

Survey Method 3 is a bias sample because only the students who are in soccer and football teams are surveyed leaving out other students doing other sports.

STEP 4: Answer Question C

Another survey method the manager could use that will create a random sample is surveying 50 students to find out their favorite teachers in the school.

STEP 5: Answer Question D

The larger the sample, the more likely it will be representative of the population. Although, beyond a certain point, the results won't change much, so 80 is probably enough. put them in numerical order from least to greatest.

80 sample size is enough to represent the population.

9

Explanation

Step 1

the absolute value or modulus of a real number x, denoted |x|, is the non-negative value of x without regard to its sig, it means you allways will get a positive number

examples

[tex]\begin{gathered} \lvert5\rvert=5 \\ \lvert-5\rvert=5 \\ \lvert-356\rvert=356 \\ \lvert107\rvert=107 \\ \lvert-107\rvert=107 \\ \text{and so on} \end{gathered}[/tex]

Step 2

Apply to solve

[tex]\lvert-12\rvert-\lvert-3\rvert[/tex][tex]\begin{gathered} \lvert-12\rvert=12 \\ \lvert-3\rvert=3 \end{gathered}[/tex]

now, replace

[tex]\lvert-12\rvert-\lvert-3\rvert=12-3=9[/tex]

so, the answer is

[tex]9[/tex]

I hope this helps you

Centre = (0, 0) and radius = 4

The equation of a circle is given as

(x - h)^2 + (y -k)^2 = r^2

We are given the equation

(x - 0)^2 + (y - 0)^2 = r^2

h = 0 and k = 0

r^2 = 16

r = 4

Hence, the centre of the circle is (0, 0) and radius = 4

Solution

For this case we can do the following:

[tex]\frac{6}{3}=\frac{1}{3}m^2-10[/tex]

And then we can do this, adding 10 in both sides:

[tex]2+10=\frac{1}{3}m^2[/tex]

Then we can multiply both sides by 3 and we got:

[tex]36=m^2[/tex]

Then we can take square root in both sides and we got:

[tex]m=\sqrt[]{36}[/tex]

And then the solution would be:

[tex]m=6,m=-6[/tex]

Given:

Let y be the number of cats in x years.

Cat population on Purr Island:

[tex]undefined[/tex]

0.29

Explanation

Step 1

the probability of an event is the likelihood of that event occuring. Probability is a value between (and including) zero and one

[tex]P=\frac{favorabl\text{e outcomes}}{\text{total outcomes}}[/tex]

event1: a student getting an A in mathematics

The probability of a student getting an A in mathematics

is 0.14

[tex]\begin{gathered} P(A)=0.14 \\ \end{gathered}[/tex]

and

event b:a student getting an A in chemistry

The probability a student not getting an A in

chemistry is 0.85,it means the probability a student getting an A is 0.15.

[tex]P(B)=0.15[/tex]

hence,

the probability that a student will get an A

in mathematics or chemistry is

[tex]P(A\text{ or B)=P(A)+P(B)=0.14+0.15=0.29 }[/tex]

I hope this helps you

Answer:

0.29

Step-by-step explanation:

Notice that the total amount of people on the survey is 100. Since there are 48 girls in total, then the total amount of boys must be 52.

For the total of boys to add up to 52, there must be 52-16-27=9 boys whose favorite flavour is Strawberry.

For the total of girls to add up to 48, there must be 48-19-19=10 girls whose favorite flavour is Vanilla.

Adding the corresponding values for each column, we can see that the Total row should be filled as follows:

Vanilla: 10+16 = 26

Mint: 19+27 = 46

Strawberry: 19+9 = 28

The most liked flavour is Mint, and the least liked flavour is Vanilla.

We will have that the front wheels of the car would carry the following weight:

[tex]w=\frac{3860\cdot54}{100}\Rightarrow w=\frac{10422}{5}\Rightarrow w=2080.4\Rightarrow w\approx2080[/tex]

So, the front wheels carry approximately 2080 Lb of the total weigth.

hello

to find the slope of the line CD, let's use the formula of slope

[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ y_2=13 \\ x_2=5 \\ y_1=-7 \\ x_1=1 \end{gathered}[/tex]

now we can simple input the values and solve for slope (m)

[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{13-(-7)}{5-1} \\ m=\frac{20}{4} \\ m=5 \end{gathered}[/tex]

from the calculation above, the slope of the line CD is equal to 5

(a) Given this equation of a line:

[tex]y-7x-6=0[/tex]

You need to rewrite it in Slope-Intercept Form:

[tex]y=mx+b[/tex]

Where "m" is the slope of the line and "b" is the y-intercept.

You can rewrite it in this form by solving for "y":

[tex]\begin{gathered} y-7x=6 \\ y=7x+6 \end{gathered}[/tex]

You can identify that the y-intercept is:

[tex]b=6[/tex]

Then, you can write the following equation of a line with the same y-intercept:

[tex]y=x+6[/tex]

(b) Given the line:

[tex]7x-9y=9[/tex]

You can rewrite it in Slope-Intercept Form in order to identify its slope:

[tex]-9y=-7x+9[/tex][tex]\begin{gathered} y=\frac{-7}{-9}x+\frac{9}{(-9)} \\ \\ y=\frac{7}{9}x-\frac{9}{9} \\ \\ y=\frac{7}{9}x-1 \end{gathered}[/tex]

You can identify that its slope is:

[tex]m=\frac{7}{9}[/tex]

By definition, the slopes of parallel lines are equal, but the y-intercepts are different.

Therefore, knowing this, you can write the following equation of a line parallel to the line given in the exercise:

[tex]y=\frac{7}{9}x+1[/tex]

Hence, the answers are:

(a)

[tex]y=x+6[/tex]

(b)

[tex]y=\frac{7}{9}x+1[/tex]

The following parameters are provided in the question:

[tex]\begin{gathered} \text{Principal, P= \$1200} \\ \text{Time, T=1 year} \\ \text{Rate, R=59\%} \end{gathered}[/tex]

The simple interest is given by the formula:

[tex]I=\frac{PRT}{100}[/tex]

Thus,

[tex]\begin{gathered} I=\frac{1200\times59\times1}{100} \\ I=\text{ \$708} \end{gathered}[/tex]

The amount, A, payable in one year is given as:

[tex]\begin{gathered} \text{Amount}=\text{Principal}+\text{Interest} \\ A=1200+708 \\ A=\text{ \$1908} \end{gathered}[/tex]

Answer:$1908

Step-by-step explanation:

Triangles are congruent when they have exactly the same three sides and exactly the same three angles.

From the image given in the question, we can infer that only a side and an angle is congruent to another side, and the angle

Hence, the condition for congruency (Having exactly 3 sides and 3 angles) is not satisfied

Given,

The total population of a city has 390,000.

Each year population grows by 3.75%.

To find: The population after 10 years.

Solution:

The population after ten years is

[tex]\begin{gathered} 390,000\times(1+\frac{3.75}{100})^{10} \\ =390,000\times(\frac{103.75}{100})^{10} \\ =390,000\times1.0375 \\ =404,625 \end{gathered}[/tex]

Hence, the answer is 404,625.

To find how can the transformation be represented algebraically, compare two corresponding point, for example, B and B'.

Coordinates of B are (5, -3) and coordinates of B' are (-2, 0).

Now, what is necessary for 5 to became -2? To substract 7.

What is necessary for -3 to became 0? To add 3.

Then, the transformation is:

[tex](x-7,y+3)[/tex]

The correct answer is (X-7, Y+3)

Let's solve the equation:

[tex]\begin{gathered} -7(1-4x)=13(2x-3) \\ -7+28x=26x-39 \\ 28x-26x=-39+7 \\ 2x=-32 \\ x=-\frac{32}{2} \\ x=-16 \end{gathered}[/tex]

Therefore, x=-16.

We are asked to find the probability of getting a 2 when rolling a die, remember that a die has 6 sides, of which only one side has the number 2 on it.

That is to say, we must find the probability that a side comes out of the 6 sides.

This probability is expressed as the chances of the desired event happening among all the possibilities, that is 1 divided by 6.

In conclusion, the answer is:

[tex]\frac{1}{6}[/tex]

Answer:

Slope = 1

Explanation:

The slope of a line can be calculated using two points in the line (x1, y1) and (x2, y2) as follows:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Then, if we take two points in the line like (0, 3) and (2, 5) and we replace (x1, y1) and (x2, y2) respectively, we get that the slope is equal to:

[tex]m=\frac{5-3}{2-0}=\frac{2}{2}=1[/tex]

So, the slope of the line on the graph is 1

In Hypothesis Testing it is required to formulate the two or more statements, so the answer to the question is option b) Claim.

Jerb, this is the solution:

Cups of water are the same amount as the number of servings, as you can see in the table.

Cups of frozen juice are double the number of cups of water.

In consequence the correct ratio for 5 servings is:

5 : 10