Answers
The value of x nodes given quadrilateral is 80° which is determined by the measure of the supplemental interior angle.
What is the quadrilateral?A quadrilateral is a polygon with four sides. This also indicates that a quadrilateral has four vertices and four angles.
Exterior Angle is defined as an angle produced on the outside of a polygon by extending the sides of the polygon.
First, we have to find the measure of the supplemental interior angle
Here take the exterior angle1 = 100° and exterior angle2 = 60°, find its interior angles
⇒ 100 + int.1 = 180 ⇒ int.1 = 180 - 100 = 80°
⇒ 60 + int.2 = 180 ⇒ int.2 = 180 - 60 = 120°
Since the sum of all interior angles of a polygon = 360°
As per the given figure,
x + 80 + x + 120 = 360
2x = 360 - 200
2x = 160
x = 80°
Therefore, the value of x nodes given quadrilateral is 80°.
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Related Questions
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
Answers
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))
How do you write 6 tens + 4 ones + 5 tenths + 2 hundredths + 8 thousandths
Answers
Answer:64.528 is the decimal
Step-by-step explanation:
Nick skates 2 1/8 miles in 1/2 of an hour. What is Nick's average speed, in miles per hour ?
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Average speed = distance / time
From the question;
distance = 2 1/8 miles = 17/8 miles
time = 1/2
substitute the values into the formula;
[tex]\text{Average sp}eed\text{ =}\frac{\frac{17}{8}}{\frac{1}{2}}[/tex][tex]=\frac{17}{8}\times\frac{2}{1}[/tex][tex]=\frac{17}{4}[/tex][tex]=4\frac{1}{4}\text{ miles per hour}[/tex]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.
Answers
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]Are the answers to question six part a b c and d correct?
Answers
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?
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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.
Given f(x)=6(1-x), what is the value of:a) f(-8)_____b) f(x) = -30 _____c) f(x) = 30____d) f(30)_____
Answers
Answer:
a) f(-8) = 54
b) f(x) = -30, x = 6
c) f(x) = 30, x = -4
d) f(30) = -174
Explanation:
Given the function:
f(x) = 6(1 - x)
To find f(-8), we replace x by -8 in the equation and then solve
f(-8) = 6[1 - (-8)8]
= 6(1 + 8)
= 6(9)
= 54
For f(x) = -30, we replace f(x) by -30 and solve for x
-30 = 6(1 - x)
Divide both sides by 6
1 - x = -30/6 = -5
Subtract 1 from both sides
-x = -6
Multiply both sides by -1
x = 6
For f(x) = 30, we replace f(x) by 30 and solve for x
30 = 6(1 - x)
Divide both sides by 6
1 - x = 30/6 = 5
Subtract 1 from both sides
-x = 4
Multiply both sides by -1
x = -4
f(30) = 6(1 - 30)
= 6(-29)
= -174
Solve 7x-2y = 17 for y
Answers
hello
the question here is an equation and we are asked to solve for y
we'll follow some steps here
[tex]7x-2y=17[/tex]step 1
take y to the left side of the equation and bring 17 to the right hand side of the equation
note: the sign changes once they cross equality sign
[tex]\begin{gathered} 7x-2y=17 \\ 7x-17=2y \end{gathered}[/tex]step 2
divide both sides by the coeffiecient of y which is 2
[tex]\begin{gathered} 2y=7x-17 \\ \frac{2y}{2}=\frac{7x-17}{2} \\ y=\frac{7x-17}{2} \end{gathered}[/tex]from the calculations above, the value of y = (7x - 17)/2
If 260 is decreased by 65%, what is the new amount?
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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.
How do I solve for x? Would my answer be 27?
Answers
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]Question 2 (7 points)Match the fractions and decimals to the corrects percentage.
Answers
we can change a fraction to a percentage multiplying the fraction by 100
also, we can change a decimal number to a percentage multiplying by 100
for example
1. 1/5
[tex]\frac{1}{5}\cdot100=20[/tex]In this case, 1/5 represent 20%
4. .625
[tex]0.625\cdot100=62.5[/tex]In this case, 0.625 represent 62.5%
If we do the same process to all the next numbers we will obtain the next solutions.
1. 1/5 ------ a. 20%
2. 8/10 ------ f. 80%
3. 0.08 ------ d. 8%
4. .625 ---- g. 62.5%
5. 32/100 ---- b. 32%
6. 1/2 ------ c. 50%
7. 1.25 ---- e. 125%
How many apple pies did they sell and how many blueberry pies did they sell?
Answers
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
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
Answers
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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What is the volume of the figure in cubic inches?
Answers
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]there are 66 utensils in the cafeteria. 22 of them are spoons and the rest are Forks. what is the ratio of the number of spoons to the total number of utensils?And what is the ratio of the number of forks to the number of spoons?
Answers
Let's begin by listing out the information given to us:
Total utensils = 66
Spoons = 22
Forks = 66 - 22 = 44
The ratio of spoons to the total utensil is given by the ratio of spoons to total utensils. We have:
22:66 ⇒ 1:3
Therefore, the ratio of spoons to total utensils is 1 spoon is to 3 utensils
The ratio of the number of forks to spoon is given by the ratio of forks to spoon. We have:
44:22 ⇒ 2:1
Therefore, the ratio of forks to spoon is 2 to 1. For every 2 forks, there is 1 spoon
if 1ml = 0.00011 then 9ml= _____
Answers
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
0.00099Solve the equation by identifying the quadratic form. Use a substitute variable(t) and find all real solutions by factoring. Type your answers from smallest to largest. If an answer is not an integer then type it as a decimal rounded to the nearest hundredth. When typing exponents do not use spaces and use the carrot key ^ (press shift and 6). For example, x cubed can be typed as x^3.x^{10}-2x^5+1=0Step 1. Identify the quadratic formLet t= Answer. We now have:t^2-2t+1=0Step 2. FactorFactor this and solve for t to get t=Answer Step 3. Solve for xWe have solved for t now we need to use this value for t to help us solve for x. Revisit step 1 to remind you of the relationship between t and x. Type your real solutions (no extraneous) from smallest to largest.x= Answer
Answers
Given:
[tex]x^{10}-2x^5+1=0[/tex]Step 1: To identify the quadratic form of the given equation.
[tex]\begin{gathered} x^{10}-2x^5+1=0 \\ (x^5)^2-2x^5+1=0 \\ \text{Put x}^5=t,\text{ it gives} \\ t^2-2t+1=0 \end{gathered}[/tex]So, t = x²
Step 2: Factor the quadratic equation in step 1.
[tex]\begin{gathered} t^2-2t+1=0 \\ t^2-t-t+1=0 \\ t(t-1)-t(t-1)=0 \\ (t-1)(t-1)=0 \end{gathered}[/tex]Thus, the factors of the equation is
[tex](t-1)(t-1)=0[/tex]Step3: solve for x.
[tex]\begin{gathered} (t-1)(t-1)=0 \\ (x^5-1)(x^5-1)=0 \\ \Rightarrow x^5-1=0,x^5-1=0 \\ \Rightarrow x=1 \end{gathered}[/tex]Answer: x = 1
Garvin earned $ 948.35 in net pay for working 24 hours. He paid $ 348.26 in federal and state taxes, and $ 145.06 in FICA taxes. What is Garrett's hourly wage? Round your answer to two decimal places. If answer doesn't have two decimal places include zeros to make two decimal places. For the units, use a word not a symbol. Be sure to attach your work to this question in order to receive credit for your answer.Your Answer:units:
Answers
ANSWER:
18.96 dollars per hour
STEP-BY-STEP EXPLANATION:
The 24-hour salary is calculated with the earnings and we subtract the taxes, as follows:
[tex]\begin{gathered} s=948.35-348.26-145.06 \\ s=455.03 \end{gathered}[/tex]Now, we divide by 24 to find out Garvin's hourly wage:
[tex]\begin{gathered} h=\frac{455.03}{24} \\ h=18.96 \end{gathered}[/tex]Therefore, the hourly wage is $18.96.
a standard Normal distribution, what percentage of observationnd the z-table here.4.95%5.48%6.06%95.05%
Answers
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%
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.
Answers
Answer:
C. The graph of f(x) is shifted 17 units up.
Step-by-step explanation:
When + is outside the equation, it means up.
what is the slope of (12 -18) (-15 -18)
Answers
Answer:
m = 0
Step-by-step explanation:
[tex]m=\frac{-18-(-18)}{-15-12)} \\m=\frac{0}{-27} \\m= 0/-27 = 0\\m=0[/tex]
I believe the answer to be c but I'm not the best at word problems this is a practice study guide.
Answers
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)
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
Answers
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.
Write the percent as fraction or mixed number in simplest form 750%
Answers
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]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?
Answers
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.
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
Answers
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
- 32 + 2Determine for each 2-value whether it is in the domain of f or not.In domainNot in domain203
Answers
f(x) = x-3 / x+2
To be in the domain, we have to avoid 0 on the bottom of the fraction.
So, the bottom of the fraction is x+2.
x=-2
(-2)+2= 0
-2 is not in the domain
x= 0
(0)+2= 2
0 is in the domain
x=2
(2)+2=4
I just need help finding the area of shape c.
Answers
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.
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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]Answer7023.85Evaluate 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) ≈
Answers
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 farmer is planning on picking 1,000 bell peppers on the first day of the harvest. After picking the first 600, he finds that 70 percent of them are green and 30 percent of them are red. How many of the remaining peppers must he pick must be red in order for exactly half of the total number of peppers picked to be red?
Answers
Answer:
320 red bell peppers
Step-by-step explanation:
First, let's calculate how many green and red bell peppers the farmer harvest in the first time:
Green peppers: 600*70/100 = 420
Red peppers: 600*30/100 = 180
If the farmer wants that half (50%) of the pepper harvest are red:
The total number of red peppers harvest have to be:
100*50/100 = 500
For this reason, the amount of remaining red peppers that have to be harvest are:
500 - 180 = 320
Answer: The farmer has to harvest more 320 red bell peppers