38
1) Starting from the first equation
3x +6 = 18 Subtract 6 from both sides
3x = 18 -6
3x = 12 Divide both sides by 3
x =4
2) Since x =4, let's plug that into the second expression 10x -2 to find out "what is 10x -2"
10x -2 Replace x, by 4
10(4) -2 Effectuate the multiplication
40 -2
38
Hence, the answer is 38
I need help with a word problem in algebra 2 please
We were given the following information:
Plan 1
Cost = $175
It has unlimited call & texts as well as 15gb
Plan 2
Cost = $50 per month
It has unlimited call & texts as well as 6gb
After 6gb, data is charged $5 per gb
From this we have the following equations:
[tex]undefined[/tex]There are 73 students in a classroom, and the desired ratio of students to computers is 6 to 1. How many computers are needed to achieve the desired ration?
Answer: 12
Explanation:
Given:
Total number of students in a classroom = 73
Ratio of students to computers = 6:1
To find the number of computers needed to achieve the desired ration, we use the ratio:
[tex]\begin{gathered} \frac{\text{Total number of students}}{\text{Total number of computers}}=\frac{6}{1} \\ We\text{ plug in what we know} \\ \frac{\text{7}3}{\text{Total number of computers}}=\frac{6}{1} \\ \text{Simplify and rearrange} \\ \text{Total number of computers = 73(}\frac{1}{6}) \\ \text{Calculate} \\ T\text{otal number of computers = }12.16\text{ =12} \\ \end{gathered}[/tex]Therefore, the number of computers needed is 12.
If 260 is decreased by 65%, what is the new amount?
To find the new amount, substract the percent of the original amount to the original amount, this way:
[tex]260-0.65\cdot260=91[/tex]The new amount is 91.
Question 23 of 25
What is the effect on the graph of f(x) = when it is transformed to
g(x) = +17?
A. The graph of f(x) is shifted 17 units down.
B. The graph of f(x) is shifted 17 units to the right.
OC. The graph of f(x) is shifted 17 units up.
OD. The graph of f(x) is shifted 17 units to the left.
Answer:
C. The graph of f(x) is shifted 17 units up.
Step-by-step explanation:
When + is outside the equation, it means up.
A simple random sample from a population with a normal distribution of 98 body temperatures has x=98.20°F and s=0.61°F. Construct a 99% confidence interval estimate of the standard deviation of body temperature of all healthy humans. Click the icon to view the table of Chi-Square critical values. °F
from the question;
we are to construct 99% confidence interval. this can be done using
[tex]\bar{}x\text{ }\pm\text{ z}(\frac{s}{\sqrt[]{n}})[/tex]where,
[tex]\bar{x}\text{ = }98.20,\text{ s = 0.61, n = 98 z= 2.576}[/tex]inserting values
[tex]\begin{gathered} 98.20\text{ }\pm2.576\text{ }\frac{0.61}{\sqrt[]{98}} \\ 98.20\text{ }\pm\text{ 2.576}\times0.0616 \\ =\text{ 98.20 }\pm\text{ }0.159 \\ =98.20\text{ + }0.159\text{ or 98.20 - 0.159} \\ =\text{ 98.359 0r 98.041} \end{gathered}[/tex]therefore the 99% confident inter vale is between 98.041 to 98.359
simplify -5m²n³ × 15m⁴ n⁶
To simplify the given expression we will use the following property of exponents:
[tex]a^n\times a^m=a^{n+m}.[/tex]Using the above property we get:
[tex]-5m^2n^3\times15m^4n^6=(-5\times15)m^{2+4}n^{3+6}=-75m^6n^9.[/tex]Answer:
[tex]-5m^2n^3\times15m^4n^6=-75m^6n^9.[/tex]Write the percent as fraction or mixed number in simplest form 750%
Answer
[tex]7\frac{1}{2}[/tex]Explanation
The 750 percent as a fraction or mixed number in simplest form is calculated as follows:
[tex]750\%=\frac{750}{100}=\frac{75}{10}=\frac{15}{2}=7\frac{1}{2}[/tex]Solve the inequality: y-5-20Which of the following is the graph of the solution?
Given the inequality:
[tex]y-5>-20[/tex]Let's select the graph which represents the solution.
Let's solve the inequality.
Add 5 to both sides of the inequality:
[tex]\begin{gathered} y-5+5>-20+5 \\ \\ y>-15 \end{gathered}[/tex]Since y is greater than -15, the graph of the inequality will be a number line which has an open dot at the point -15, then shaded to the right of the number line.
Therefore, the graph of the solution is:
ANSWER:
A
Jacob opened his piggy bank and found Nickels, Dimes, and Quarters totaling 81 coins. The total value of the coins was $7.90. The number of Dimes was 7 less than triple the number of Quarters. Write a system of equations that represents this situation. Use N, D, and Q.
A Nickel is 5 cents = 5/100 = $0.05
A dime is 10 cents = 10/100 = $0.1
A quarter is 25 cents = 25/100 = $0.25
Let N represent the number of nickels
Let D represent the number of dimes
Let Q represent the number of quarters
Jacob opened his piggy bank and found Nickels, Dimes, and Quarters totaling 81 coins. It means that
N + D + Q = 81
The total value of the coins was $7.90. It means that
0.05N + 0.1D + 0.25Q = 7.9
The number of Dimes was 7 less than triple the number of Quarters. It means that
D = 3Q - 7
The system of equations is
N + D + Q = 81
0.05N + 0.1D + 0.25Q = 7.9
D = 3Q - 7
How many apple pies did they sell and how many blueberry pies did they sell?
Let the number of apple pies x
Let the number of blue pies y
Since they sold 38 pies on Saturday, then
Add x and y, then equate the sum by 38
[tex]x+y=38\rightarrow(1)[/tex]Since they sold each apple pie for $11 and each blueberry pie for $13
Since they collected $460 on Saturday, then
Multiply x by 11 and y by 13, then add the products and equate the sum by 460
[tex]11x+13y=460\rightarrow(2)[/tex]Now, we have a system of equations to solve it
Multiply equation (1) by -13 to equate the coefficients of y in values and opposite them in signs to eliminate them
[tex]\begin{gathered} (-13)(x)+(-13)(y)=(-13)(38) \\ -13x-13y=-494\rightarrow(3) \end{gathered}[/tex]Add equations (2) and (3)
[tex]\begin{gathered} (11x-13x)+(13y-13y)=(460-494) \\ -2x+0=-34 \\ -2x=-34 \end{gathered}[/tex]Divide both sides by -2
[tex]\begin{gathered} \frac{-2x}{-2}=\frac{-34}{-2} \\ x=17 \end{gathered}[/tex]Substitute the value of x in equation (1) to find y
[tex]17+y=38[/tex]Subtract 17 from both sides
[tex]\begin{gathered} 17-17+y=38-17 \\ y=21 \end{gathered}[/tex]The y sold 17 apple pies and 21 blueberry pies
The answer is the last choice
What is the volume of the figure in cubic inches?
Solution
First, we need to convert the dimensions in feet to inches
[tex]\begin{gathered} \text{ since } \\ 1\text{ ft}=12\text{ inches} \\ \\ \Rightarrow1.5\text{ ft}=1.5\times12\text{ inches}=18\text{ inches} \\ \Rightarrow0.5\text{ ft}=0.5\times12\text{ inches}=6\text{ inches} \end{gathered}[/tex]Hence, the volume is;
[tex]V=l\times b\times h[/tex][tex]V=4\times18\times6=432\text{ inches cubic}[/tex]Please help nobody knows the answer to my question. Round to 2 decimal places.
To answer this question we will use the z-score.
Recall that the z-score is given as follows:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma}, \\ \text{where x is the observed value, }\mu\text{ is the mean, and }\sigma\text{ is the standard deviation.} \end{gathered}[/tex]The z-score of 54 is:
[tex]z=\frac{54-50}{5}=\frac{4}{5}=0.8.[/tex]The z-score of 56 is:
[tex]z=\frac{56-50}{4}=\frac{6}{5}=1.2.[/tex]Now, the probability of flipping 54, 55, or 56 heads is the same as the following probability:
[tex]P(0.8Now, recall, that:[tex]P(aNow, from the given table we get that:[tex]\begin{gathered} P(0.8)=0.7881, \\ P(1.2)=0.8849. \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} P(0.8Answer: 0.10.A rectangular pool is 7 meters wide and 12 meters long. If you swim diagonally from one corner to the other, how many meters will you swim? Approximate the answer to the nearest tenth.
Answer: 15cm
Step-by-step explanation:
Your welcome
If Tanisha wants the top of the ladder to reach exactly 8 feet up the building, what is X, the distance between the building and the base of the ladder in feet?
Solution:
Given:
The right triangle can be sketched as shown below;
To get the distance between the building and the base of the ladder, we use the Pythagoras theorem since it is a right triangle.
[tex]\begin{gathered} \text{hypotenuse}^2=\text{adjacent}^2+\text{opposite}^2 \\ \\ \text{where;} \\ \text{hypotenuse}=10 \\ \text{adjacent}=x \\ \text{opposite}=8 \end{gathered}[/tex]
Hence,
[tex]\begin{gathered} \text{hypotenuse}^2=\text{adjacent}^2+\text{opposite}^2 \\ 10^2=x^2+8^2 \\ 100=x^2+64 \\ 100-64=x^2 \\ 36=x^2 \\ x=\sqrt[]{36} \\ x=6 \end{gathered}[/tex]Therefore, the distance between the building and the base of the ladder in feet is 6 feet.
720÷5 WORK OUT NEEDED
144
Explanation:[tex]720\text{ }\div\text{ 5}[/tex]working the division:
The process:
7 ÷ 5 = 1 R 2
add the 2 to the next number: this gives 22
22 ÷ 5 = 4 R 2
add 2 to the next number: this gives 20
20 ÷ 5 = 4 R 0
The result of 720 ÷ 5 = 144
The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
50 X 5 X 3
answer divide
by 36
How do I solve for x? Would my answer be 27?
SOLUTION
Exterior property of a triangle
An exterior angle of a triangle is equal to the sum of its two opposite non-adjacent interior angles.
Hence,
[tex](5x+13)^0=(4x+2)^0+(2x-9)^0[/tex]Simplify and evaluate for x
[tex]\begin{gathered} 5x+13^0=4x+2^0+2x-9^0 \\ 5x+13^0=4x+2x+2^0-9^0 \\ 5x+13^0=6x-7^0 \\ \text{Collect like terms} \\ 13^0+7^0=6x-5x \\ 20^0=x \\ \therefore x=20^0 \end{gathered}[/tex]Therefore,
[tex]x=20^0[/tex]write in point slpoe form an equation of the line that passes through th griven point and has the given slope (1, -3); m = 4
A linear equation in slope-point form looks like this:
y -y0= m(x-x0)
Where m is the slope of the line and (x0,y0) is a point of the line.
In this case, we know that the slope of the line equals 4 and that the line goes through the point (1, -3), then, we can substitute these values into the general form to get:
y-(-3) = 4(x-(1))
Does anyone know the answer to this?
The most appropriate choice for equation of line in slope intercept form will be given by
x + 2y = -16 is the required equation of line
What is equation of line in slope intercept form?
Equation of line in slope intercept form is given by y = mx + c
Where, m is the slope of the line and c is the y intercept of the line
The distance from the origin to the point where the line cuts the x axis is called x intercept
The distance from the origin to the point where the line cuts the y axis is called y intercept
Slope of a line is the tangent of the angle which the line makes with the positive direction of x axis
If [tex]\theta[/tex] is the angle which the line makes with the positive direction of x axis, then slope of the line is given by
[tex]m=tan\theta[/tex]
If the line passes through ([tex]x_1, y_1[/tex]) and ([tex]x_2, y_2[/tex])
slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Here,
The line passes through (0, -8) and (-2, -7)
Slope =
[tex]\frac{-7 -(-8)}{-2-0}\\-\frac{1}{2}[/tex]
The line passes through (0, -8)
Equation of line
[tex]y - (-8) = -\frac{1}{2}(x - 0)\\\\y + 8 = -\frac{1}{2}x\\2y + 16 = -x\\x + 2y = -16[/tex]
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Let a represent the row number in this pattern. Write a rule that tells you the number of dots, d, in row n (Hint: Your rule should begin with "d=") Row 1 Row 2 Row 3 Row 4
The rule to show the number of dots in the pattern is
d = 2aWhat is a pattern?A pattern is a repetition of items, when the repetition is in ordered then the pattern can be forecasted.
The given pattern is ordered by the rule at which it was formed. The rule helps to forecast the number of dots in the next row
How to get the rules of the patternThe information given in the question include:
Let a represent the row number in this patternA picture image shoeing the rows and dotsYour rule should begin with "d="row 1 = 2 dots
row 2 = 4 dots
row 3 = 6 dots
it can be seen that
2 * number of rows = number of dots
Hence:
d = 2 * a
d = 2a
checking the rule for the 4th row
d = 2 * 4
d = 8
counting the dots confirms the rule is okay
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if 1ml = 0.00011 then 9ml= _____
if 1ml = 0.00011 then 9ml=
Apply proportion
0.00011/1=x/9
solve for x
x=9*0.00011
x=0.00099
answer is
0.00099If 6 is subtracted from the third of three consecutive odd integers and the result is multiplied by 2, the answer is 23 less then the sun if the first and twice the second of the integers
Divide 8 A) 3 B) 0) 7 16 D) 7. 32
Answer
3(1/2) or (7/2) or 3.5
Step-by-step Explanation
The question wants us to divide (7/8) by (1/4).
[tex]\frac{7}{8}\div\frac{1}{4}[/tex]The first step to solving division when it comes to fractions is to change the division sign to multiplication sign, which changes the fraction after the division sign to its inverse.
That is, in changing ÷ into ×, (1/4) changes to (4/1)
So,
[tex]\begin{gathered} \frac{7}{8}\div\frac{1}{4} \\ =\frac{7}{8}\times\frac{4}{1} \\ =\frac{28}{8} \\ =\frac{7}{2} \\ =3\frac{1}{2} \end{gathered}[/tex]Hope this Help!!!
a standard Normal distribution, what percentage of observationnd the z-table here.4.95%5.48%6.06%95.05%
SOLUTION:
Case: Z-scores and probabilities
Given: z-score of standard normal distribution, z= 1.65
Required: To get the percentage of observation
Method: We will be reading it off the z-score table
Step 1: First we see what the table looks like
Step 2: From the table, we trace 1.65 by looking at 1.6 on the column title and 0.05 on the row title
Step 3: We observe the value is 0.4505
This translates to 45.05%.
However, we are interested in the values above the 45.05%. So everything from the left of that line to the 50th percentile is 45.05% of the populations. In addition to that you have another 50% of the people below the 50th percentile. That's a total of 95.05% below this z score
To get the z-score above this, we do:
1 - 0.9505
P(> z) = 0.0495 or 4.95%
Final answer:
A) The answer is 4.95%
A study of consumer smoking habits includes 177 people in the 18-22 age bracket ( 48 of whom smoke), 146 people in the 23-30 age bracket ( 31 of whom smoke), and 81 people in the 31-40 age bracket ( 28 of whom smoke). If one person is randomly selected from this sample, find the probability of getting someone who is age 18-22 or does not smoke.A. 0.319B. 0.854C. 0.173D. 0.729
From the question,
Age 18 - 22 has 177 people, 48 of whom smoke.
Age 23-30 has 146 people, 31 of whom smoke.
Age 31-40 has 81 people, 28 of whom smoke.
People who do not smoke = (177- 48)+(146-31)+(81-28) = 129 + 115 +53 = 297 people.
People within age 18-22 who do not smoke = 129
Total number of events = 404
[tex]\begin{gathered} p(18-22\text{ or does not smoke) = }\frac{(177+297-129)}{404} \\ p(18-22\text{ or does not smoke)}=\frac{345}{404}=0.853960396 \\ p(18-22\text{ or does not smoke)}\approx0.854 \end{gathered}[/tex]Hence, option B is the answer.
Evaluate f(2) and f(2.1) and use the results to approximate f '(2). (Round your answer to one decimal place.)f(x) = x(9 − x)f '(2) ≈
Given a function f(x) = x(9 - x).
We need to find the value of f(2) and f(2.1) and use them to approximate the value of f'(2).
The value of f(2) is calculated below:
[tex]\begin{gathered} f(2)=2(9-2) \\ =2(7) \\ =14 \end{gathered}[/tex]The value of the f(2.1) is calculated as follows:
[tex]\begin{gathered} f(2.1)=2.1(9-2.1) \\ =2.1(6.9) \\ =14.49 \end{gathered}[/tex]Now, by the definition of f'(x), we know that
[tex]f^{\prime}(x)=\frac{f(x+\Delta x)-f(x)}{(x+\Delta x)-x}=\frac{f(x+\Delta x)-f(x)}{\Delta x}[/tex]For the given condition, x = 2, and delta x = 0.1. So, the value of f'(2) is
[tex]\begin{gathered} f^{\prime}(2)=\frac{f(2+0.1)-f(2)}{0.1} \\ =\frac{f(2.1)-f(2)}{0.1} \\ =\frac{14.49-14}{0.1} \\ =\frac{0.49}{0.1} \\ =4.9 \end{gathered}[/tex]Thus, the approximate value of f'(2) is 4.9.
A box is filled with 3 yellow cards, 2 blue cards, and 7 brown cards. A card is chosen at random from the box. What is the probability that it is a yellow or abrown card?Write your answer as a fraction in simplest form.
We need to find the probability of the card chosen at random is yellow or brown.
So, since there are 3 yellow cards and 7 brown cards, the total numbers of cards that are yellow or brown is:
[tex]3+7=10[/tex]Now, the probability that the chosen card is yellow or brown can be found by dividing the above value by the total number of cards in the box.
The total number of cards in the box is:
[tex]3+7+2=12[/tex]Thus, that probability is given by:
[tex]\frac{10}{12}=\frac{10\div2}{12\div2}=\frac{5}{6}[/tex]Therefore, the answer is:
[tex]\frac{5}{6}[/tex]I just need help finding the area of shape c.
We need to find the area of Shape C.
Please have a look at the diagram below:
To find x, we can use the Pythagorean Theorem on the right triangle.
[tex]\begin{gathered} 100^2+x^2=107^2 \\ \end{gathered}[/tex]Now, let's solve for x. The steps are shown below:
[tex]\begin{gathered} 100^2+x^2=107^2 \\ x^2=107^2-100^2 \\ x^2=11449-10000 \\ x^2=1449 \\ x=\sqrt[]{1449} \\ x=38.07 \end{gathered}[/tex]So, the top part (dotted line) is
[tex]\begin{gathered} x+100+x \\ =38.07+100+38.07 \\ =176.14 \end{gathered}[/tex]Now, we have a trapezoid. Let's find the area of the trapezoid:
[tex]\begin{gathered} A=\frac{1}{2}(b_1+b_2)h \\ A=\frac{1}{2}(100+176.14)(100) \\ A=13,807 \end{gathered}[/tex]Now, we need to subtract the area labeled (K) from the area of the trapezoid found.
--------------------------------------------------------------------------------
Area k is a triangle with side lengths 117, 117, and 176.14. Let's find the area of the triangle. The diagram is shown below:
Now, we will find h, the height of the triangle using Pythagorean Theorem.
[tex]\begin{gathered} 88.07^2+h^2=117^2 \\ h^2=117^2-88.07^2 \\ h^2=5932.6751 \\ h=\sqrt[]{5932.6751} \\ h=77.02 \end{gathered}[/tex]The area of the triangle (region K) is,
[tex]\begin{gathered} A=\frac{1}{2}bh \\ A=\frac{1}{2}(176.14)(77.02) \\ A=6783.15 \end{gathered}[/tex]The area of region C is the area of trapezoid - area of region k (triangle). So, the area is >>>>
[tex]\begin{gathered} A=13,807-6783.15 \\ A=7023.85 \end{gathered}[/tex]Answer7023.85I believe the answer to be c but I'm not the best at word problems this is a practice study guide.
In order to find the interval of values where 95% of the shoe sizes lie, let's find the values of z-score that represents 2.5% to the left and 2.5% to the right of the standard distribution curve:
Looking at the z-table for the probabilities of 0.025 and 0.975, we have z1 = -1.96 and z2 = 1.96.
Now, we can calculate the values that define the interval using the formula below:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ -1.96=\frac{x-8.1}{1.47} \\ x-8.1=-2.88 \\ x=-2.88+8.1 \\ x=5.22 \\ \\ 1.96=\frac{x-8.1}{1.47} \\ x-8.1=2.88 \\ x=2.88+8.1 \\ x=10.98 \end{gathered}[/tex]Therefore the correct option is the second one. (It's the only option with very close values to the ones calculated)
HELP PLEASE!!!!!!!!!!! ILL MARK BRAINLIEST
[tex]-1\frac{3}{4}[/tex] is located at a point 1 on the number line.
1.1125 is located at point 6 on the number line.
14 / 8 is located at point 8 on the number line.
-0.875 is located at point 3 on the number line.
What are the locations of the numbers?The numbers are made up of mixed fractions, improper fractions, decimals, positive numbers and negative numbers.
A mixed number is a number that has a whole number, a numerator and a denominator. The numerator that has a smaller value than the denominator. and a proper fraction. . An example of a mixed number is 1 1/4. An improper fraction is a fraction in which the numerator is bigger than the denominator. An example of an improper fraction is 14/8.
A negative number is a number that is smaller in value than 0. Negative numbers would be to the left of zero on number line. An example of a negative number is -1.4. A positive number is a number that is greater in value than 0. Positive numbers are located to the right of 0 on the number line. An example of a positive number is 4.2.
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[tex]-1\frac{3}{4}[/tex] is located at a point 1 on the number line.
1.1125 is located at point 6 on the number line.
14 / 8 is located at point 8 on the number line.
-0.875 is located at point 3 on the number line.
What are the locations of the numbers?The numbers are made up of mixed fractions, improper fractions, decimals, positive numbers and negative numbers.
A mixed number is a number that has a whole number, a numerator and a denominator. The numerator that has a smaller value than the denominator. and a proper fraction. . An example of a mixed number is 1 1/4. An improper fraction is a fraction in which the numerator is bigger than the denominator. An example of an improper fraction is 14/8.
A negative number is a number that is smaller in value than 0. Negative numbers would be to the left of zero on number line. An example of a negative number is -1.4. A positive number is a number that is greater in value than 0. Positive numbers are located to the right of 0 on the number line. An example of a positive number is 4.2.
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