Answer:
∠ E = 70° , ∠ F = 40° , ∠ G = 70°
Step-by-step explanation:
given EF = FG then Δ EFG is isosceles with base angles congruent, that is
∠ G = ∠ E = 5n
the sum of the 3 angles in a triangle = 180°
sum the 3 angles and equate to 180
4n - 16 + 5n + 5n
14n - 16 = 180 ( add 16 to both sides )
14n = 196 ( divide both sides by 14 )
n = 14
Then
∠ E = 5n = 5(14) = 70°
∠ F = 4n - 16 = 4(14) - 16 = 56 - 16 = 40°
∠ G = 5n = 5(14) = 70°
Please help me with the question
You pick a card at random. 4 5 6 7 What is P(divisor of 24)? Write your answer as a percentage.
Answer: The percentage is a 2/4
Step-by-step explanation:
Answer:
50%
Step-by-step explanation:
You want to know the probability of drawing a divisor of 24 from the set of cards with numbers {4, 5, 6, 7}.
DivisorThe divisors of 24 in this set are 4 and 6, which comprise half the cards. As a percentage, this is ...
1/2 × 100% = 50%
The probability of picking a divisor of 24 is 50%.
Which of the following questions describes the equation 8/4 = -20?
The question that best describes the equation of a / 4 = 20 is D. What number, when divided by four, is equal to negative twenty?
How to find the equation ?The best question for the given equation is the question shown in option D. This is because we have a mystery number that we shall call, a. We then have to divide this number by 4 which would mean we then have the formula :
= a / 4
Then, when this number is divided by 4, it would give - 20 so we then have the full relationship of:
a / 4 = - 20
This number can be solved to be - 80.
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The full question is:
Which of the following questions describes the equation a/4 = -20?
What number, when multiplied by four, is equal to negative twenty?
What number, when divided by negative four, is equal to twenty?
What number, when multiplied by negative twenty, is equal to four?
What number, when divided by four, is equal to negative twenty?
HELP PLEASE IM ABOUT TO FAIL THIS
The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 0 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 10. There are two dots above 1 and 4. There are three dots above 2 and 5. There are 4 dots above 3.
Which of the following is the best measure of variability for the data, and what is its value?
The IQR is the best measure of variability, and it equals 3.
The IQR is the best measure of variability, and it equals 9.
The range is the best measure of variability, and it equals 3.
The range is the best measure of variability, and it equals 9.
The best measure of variability for the data, and its value is: D. The range is the best measure of variability, and it equals 9.
What is a line plot?In Mathematics and Statistics, a line plot simply refers a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.
From the data set, we have:
10, 1, 1, 4, 4, 2, 2, 2, 5, 5, 5, 3, 3, 3, 3
For the IQR, we have:
IQR = Third quartile (Q₃) - First quartile (Q₁)
IQR = 5 - 2
IQR = 3
For the range, we have;
Range = maximum - minimum
Range = 10 - 1
Range = 9.
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the rule is 8, 9. what is the 100th number? the sequence is. 8, 9, 8, 9, 8, 9, ...
The 100th number in the sequence 8, 9, 8, 9, 8, 9, ... is 8.
What is number?
Number is a mathematical object used to count, measure, and label. It can be represented in physical or symbolic form. Numbers are used in many different fields, including mathematics, science, engineering, economics, and finance. They are an important part of everyday life, as they help us to understand and solve problems. Numbers are also used to describe physical phenomena, such as time, distance, or temperature.
In the given sequence, the 8th and 9th numbers are 8 and 9 respectively. To determine the 100th number in the sequence, we can use a simple calculation.
To calculate the 100th number in the sequence, we need to divide 100 by 2 and round the result up to the nearest whole number if necessary. This will give us the number of complete pairs of 8 and 9 in the sequence. Since each complete pair consists of two numbers, we then multiply this result by 2 to get the total number of numbers up to and including the 100th number.
In this case, 100 divided by 2 is 50 and rounded up to the nearest whole number is 50. Multiplying this result by 2 gives us 100, which is the total number of numbers up to and including the 100th number. Since the 8th and 9th numbers in the sequence are 8 and 9 respectively, the 100th number in the sequence is 8.
In conclusion, the 100th number in the sequence 8, 9, 8, 9, 8, 9, ... is 8.
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Sickle cell anemia is known to run in a family. A pedigree chart for this family is shown below.
The parents are shown at the top and from left to right appear as a half-shaded circle next to a half-shaded square. The two are connected by a straight line. Below the parent pair is a vertical straight line connecting to the next row of circles and squares which are the offspring. Starting from left an unshaded square, half-shaded circle, another half-shaded circle, and a completely shaded square are shown. All of these are also connected by a horizontal straight line.
What percentage of the offspring have sickle cell anemia?
0%
25%
50%
100%
The percentage of offspring that have sickle cell anemia as shown by the pedigree chart is B. 25 %
How to find the percentage ?A pedigree chart employs completely shaded symbols to indicate individuals with a specific disease or condition, while half-shaded symbols represent carriers and unshaded symbols denote individuals without it.
Sickel cell anemia is represented by entirely shaded squares in this chart, thus there is one such square (#4) among the four offspring present.
The percentage is:
= (1 affected offspring / 4 total offspring) x 100
= 25%
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A discussion question should be phrased in such a way so as to avoid suggesting the _____ in the question.
A discussion question should be phrased in a neutral and non-leading manner to avoid suggesting a particular answer or viewpoint in the question.
This allows for open-ended discussion and encourages participants to think critically and form their own opinions.
For example, a poorly phrased discussion question might be "Don't you think that the government should increase funding for public schools?" This question is leading and suggests that the answerer should agree that more funding for public schools is necessary.
A better-phrased discussion question would be "What do you think should be done to improve the quality of education in public schools?" This question is open-ended and allows participants to explore various solutions and viewpoints.
By avoiding a leading or suggestive tone in discussion questions, participants are given the opportunity to express their own thoughts and ideas without feeling pressure to conform to a particular viewpoint. This ultimately leads to more productive and engaging discussions that allow for a diversity of perspectives and opinions.
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mary has $2.30 in her change purse. if she has 11 coins, which coins does she have?
Answer:
She has 8 quarters and 3 dimes.
Step-by-step explanation:
8 times .25 is equal to 2. If you add .1 times 3 to this sum you get $2.30.
consider the expression 3 * 2 ^ 2 < 16 5 andalso 100 / 10 * 2 > 15 - 3. which operation is performed last?
The comparison operation (the "<" and ">") is performed last in both expressions.
In the first expression, the order of operations (also known as PEMDAS or BEDMAS) dictates that we first evaluate the exponent, then the multiplication, and finally the comparison. So, we have:
3 * 2^2 = 3 * 4 = 12
12 < 16 is true, so the entire expression evaluates to "true".
In the second expression, the order of operations dictates that we first evaluate the division and multiplication (from left to right), then the subtraction, and finally the comparison. So, we have:
100 / 10 = 10
10 * 2 = 20
15 - 3 = 12
20 > 12 is true, so the entire expression evaluates to "true".
In both cases, the comparison operation is performed last.
Hence, The comparison operation ("<" and ">") is performed last in both expressions, after all the other operations have been evaluated according to the order of operations.
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m = 34 x 5³
11= 3³ x 52 x 11
(a) Find the Lowest Common Multiple (LCM) of m and n.
(b) Find the Highest Common Factor (HCF) of 5m and 3n.
The LCM of m and n is equal to 1215500 and the HCF of 5m and 3n is derived to be 2, using prime factorisation.
What is HCF and LCM?The H.C.F. or H.C.M defines the highest common factor present in between given two or more numbers, while L.C.M. defines the least common multiple number which is exactly divisible by two or more numbers.
Using prime factorisation:
LCM of m and n is derived as follows;
m = 2 × 5³ × 17
n = 2² × 11 × 13
LCM = 2² × 5³ × 11 × 13 × 17
LCM = 1215500
HCM of 5m and 3n is derived as follows;
5m = 2 × 5⁴ × 17
3n = 2² × 3 × 11 × 13
HCF = 2
Therefore, the LCM of m and n is equal to 1215500 and the HCF of 5m and 3n is derived to be 2, using prime factorisation.
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Find VX.
V
35⁰
VX =
A7
W
Write your answer as an integer or as a decimal rounded to the nearest tenth.
X
Submit
The value of VX is determined as 2.02 units.
What is trigonometry ratio?Trigonometry ratios are mathematical relationships between the angles and sides of a right triangle.
The short form of trig ratio is SOH CAH TOA;
SOH = opposite/hypotenuse
CAH = adjacent/hypotenuse
TOA = opposite/adjacent
The value of VX is calculated by applying trig ratio of TOA, opposite side and adjacent side.
tan 22 = VX/5
VX = 5 x tan (22)
VX = 2.02 units
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Find the image of a point A(4,-1) under the reflection on line y = 4.
The image after the reflection over the line y = 4 is (4, 9)
How to find the image after the reflection?We want to find the image of the point (4, -1) after the reflection over the line y = 4
Remember that for a general point (x, y), the reflection over the line y = a gives:
(x, a + |y - a|)
Then we will get:
(4, 4 + |4 - (-1))
(4, 4 + 5)
(4, 9)
That is the image after the reflection over the line y = 5.
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Carly is going on vacation and taking her dog Pickles along. Pickles eats 2 cups of Hungry Hound dog food each day. Carly wants to know how many days she can feed Pickles from a 14-cup bag of Hungry Hound.
The Answer should be x=4
true or false: when comparing normal distribution curves, the distribution with the largest standard will have the highest peak.
False. The peak of a normal distribution curve is determined by its mean, not its standard deviation.
The standard deviation measures the spread or variability of the distribution, with larger values indicating a wider distribution. However, the peak of the curve remains the same as long as the mean remains constant.
Therefore, when comparing normal distribution curves, the one with the highest mean will have the highest peak, regardless of the standard deviation. Additionally, it's important to remember that in a normal distribution, the peak occurs at the mean value and the curve is symmetric.
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What are the coordinates of the image of ΔABC after a dilation with center (0, 0) and a scale factor of 12?
1,2,3,4,5,6
A ( . )
B ( , )
C ( , )
Check the picture below.
If earth travels 6.7 x 10(power of 4) mph in one orbit, then how far will it travel in 5 days
If earth travels 6.7 x 10(power of 4) mph in one orbit, the Earth will travel 8.04 x 10^6 miles in 5 days.
How to determine how far will it travel in 5 daysWe can begin by converting 5 days to hours since we were given the speed in miles per hour:
1 day = 24 hours
Therefore, 5 days = 5 x 24 = 120 hours
Now we can use the formula:
distance = speed x time
distance = (6.7 x 10^4) x (120)
distance = 8.04 x 10^6 miles
Therefore, Earth will travel 8.04 x 10^6 miles in 5 days.
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Directions: Arrange and write the numbers in increasing order. This means from smallest to largest, or increasing in value.
Example:
+4, -3, +2, +10, -1 becomes -3, -1, +2, +4, +10
1. +2, -5, +3, -4, +1
2. -9, -2, +7, -6, +5
3. -5, -8, -3, +4, +3
4. +8, +5, +2, +7, -6
5. -4, +6, -6, +4, -7
6. +8, +5, +9, -6, -9
7. -7, -2, +4, -5, -1
8. +3, +5, -5, +6, +2
9. -6, +4, -8, +7, -2
10. -3, +8, -4, +1, -7
The numbers are written in increasing order as below
1. -5, -4, +1, +2, +3
2. -9, -6, -2, +5, +7
3. -8, -5, -3, +3, +4
4. -6, +2, +5, +7, +8
5. -7, -6, -4, +4, +6
6. -9, -6, +5, +8, +9
7. -7, -5, -2, -1, +4
8. -5, +2, +3, +5, +6
9. -8, -6, -2, +4, +7
10. -7, -4, -3, +1, +8
How to arrange the numbers from smallest to largestThe numbers are arranged using the concept of effect of negative sign to the value of a number.
When a large number is being attached with a negative sign the number becomes smaller. For instance 7 is larger than 3 but -7 is smaller than -3.
The numbers can be arranged by comparing with the order below
-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
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Calvin has enough cement to fill 4,500 in 3. he decides to change the length of the step so that he will use all of the cement . What will be the new length of the step?
To solve this problem, we the new length of the step should be 20 inches. the new length of the step should be 20 inches.
What is volume?
Volume of cement = length × width × height
where the volume of cement is 4,500 cubic inches and the height can be assumed to be 1 inch (since we are dealing with a step
can use the formula:
Volume of cement = length × width × height
where the volume of cement is 4,500 cubic inches and the height can be assumed to be 1 inch (since we are dealing with a step).
So we have:
4,500 = length × width × 1
Simplifying this equation, we get:
4,500 = length × width
Now, since we want to use all the cement, we can assume that the volume remains the same, i.e., 4,500 cubic inches. But we need to find a new length that will give us this volume.
Let's say the new length is L inches. Then we can write:
4,500 = L × width
To solve for L, we need to know the value of width. Unfortunately, we don't have that information. However, we do know that a step is typically wider than it is long. So we can assume that the width is greater than the length, i.e.,
width > L
Under this assumption, we can say that the maximum value of L occurs when width is minimized. In other words, we want to find the smallest possible value of width that will still give us a volume of 4,500 cubic inches.
To do this, we can factor 4,500 and look for pairs of factors that differ by the least amount. We get:
4,500 = 2 × 2 × 3 × 3 × 5 × 5 × 2
The pairs of factors that differ by the least amount are 2 and 225, since they differ by only 223. So we can take width to be 225 inches and L to be:
L = 4,500 / 225 = 20 inches
Therefore, the new length of the step should be 20 inches.
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OFFERING BRAINLIEST IF YOU ARE THE FASTEST!
solve for x and show your work!
*Round to nearest tenth.
Answer : So the value of x is 5
Step-by-step explanation:
As we know it is a right angled triangle which means that the angle from the origin(0,0) is 90 degree, so the angle right to it has a value of 37 degree and the angle above it has a value of 53 degree, and the value of sin37 degree is 3/5, So by applying Pythagoras theorem we get to know that the value of sin is actually Perpendicular by Hypotenuse, so we get to know that the value of x is actually 5 derived from it.
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student must get 80% of the questions correct. there are 90 on the test.how many questions must a student answer correctly to pass the test
Answer: 72
Step-by-step explanation: just ask safary, 80% of 90 to get 72
A student must answer 72 questions correctly out of the 90 questions on the test to achieve an 80% accuracy rate and pass the test.
To pass the test with an 80% score, a student must answer 72 questions correctly out of the total 90 questions. This can be calculated by first finding out what 80% of 90 is, which can be done by multiplying 0.8 (the decimal form of 80%) by 90:
0.8 x 90 = 72
Therefore, a student needs to answer at least 72 questions correctly to pass the test with an 80% score.
To determine the number of questions a student must answer correctly to pass the test, we will use the given criteria: the student needs to achieve 80% accuracy, and there are 90 questions on the test.
To find the required number of correct answers, we will multiply the total number of questions (90) by the percentage required to pass (80%). The formula for this calculation is:
(Number of correct answers) = (Total questions) × (Percentage required to pass)
In our case, this translates to:
(Number of correct answers) = (90) × (80%)
Converting the percentage to a decimal value by dividing it by 100, we get:
(Number of correct answers) = (90) × (0.8)
Now, we multiply the values:
(Number of correct answers) = 72
Therefore, a student must answer 72 questions correctly out of the 90 questions on the test to achieve an 80% accuracy rate and pass the test.
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question #1
Which vector translates Quadrilateral ABCD to Quadrilateral A'B'C'D' given the coordinates listed below?
(-5,4), B(-2,5), C (-3,2), D(-6, 1);A' (-6, 6), B' (-3,7), C’ (-4,4),D' (-7,3)
A = (-2,1)
v = (-1,2)
B
C = (1, -2)
v
D
=(2, -1)
The translation vector that translates Quadrilateral ABCD to Quadrilateral A'B'C'D' is (-4, 5).
A mathematical vector called a translation vector expresses how far one point or object is moved away from another in a specific direction. To put it another way, it is a vector that shows how far and in which direction an item or point is moved from one position to another.
Subtract the corresponding vertices of the two quadrilaterals to determine the vector that converts Quadrilateral ABCD to Quadrilateral A'B'C'D'.
Let's consider vertex A:
Translation vector = A' - A
= (-6, 6) - (-2, 1)
= (-6+2, 6-1)
= (-4, 5)
Therefore, the translation vector that translates Quadrilateral ABCD to Quadrilateral A'B'C'D' is (-4, 5).
Similarly, we can find the translation vectors for vertices B, C, and D:
For vertex B: Translation vector = B' - B = (-3, 7) - (-2, 5) = (-1, 2)
For vertex C: Translation vector = C' - C = (-4, 4) - (-3, 2) = (-1, 2)
For vertex D: Translation vector = D' - D = (-7, 3) - (-6, 1) = (-1, 2)
All the translation vectors have the same value (-1, 2), which means that the two quadrilaterals are translated by the same amount in the x and y directions.
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Gilles and aleena are arranging an academic and sports award banquet they know how many guest are going to be seated in different tables arrangement
The number of guests that can sit in each arrangement, given the diagram would be:
1 table - 6 guests2 tables - 10 guests3 tables - 14 guestsHow to find the number of guests ?To find the number of guests that are able to sit in each arrangement, you can look at the number of dots around each table arrangement on the diagram.
What we see is that for 1 table, six guests are able to sit around the table. When there are 2 tables, around 10 guests can sit around the table. This number increases by 4 to fourteen when there are 3 tables put together as shown in the diagram.
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There are 24 girls and 14 boys on a school bus. Three students are randomly selected and replaced. When finding the probability of selecting 2 girls and 1 boy, identify the compound events.
The probability of these three events occurring together is 14.7%.
The compound events involved in selecting 2 girls and 1 boy are:
Choosing a girl on the first draw, with a chance of 24/38 (due to the fact that, after one student has been chosen and replaced, there are 24 girls and 38 total passengers on the bus).
The likelihood of choosing a different girl on the second draw is 24/38 (because there are still 24 girls and 38 overall students on the bus after two pupils have been chosen and replaced).
Choosing a boy on the third draw, with a chance of 14/38 (due to the fact that there are now 14 boys and 38 total students on the bus after three kids were chosen and replaced).
To find the probability of these three events occurring together (i.e., selecting 2 girls and 1 boy), we multiply their probabilities:
P(2 girls and 1 boy) = (24/38) * (24/38) * (14/38)
= 0.14696019828, or approximately 14.7%.
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You are presented with a deck of 20 cards, numbered from 1 to 20 and can draw one card. If the number is odd, you win $13. If the number is even, you win nothing. If you play the game, what is the expected payoff? $
Answer:
Step-by-step explanation:
To calculate the expected payoff, we need to multiply the amount won by the probability of winning, and then add up all the results.
There are 10 odd numbers and 10 even numbers in the deck, so the probability of drawing an odd number is 10/20 = 1/2, and the probability of drawing an even number is also 1/2.
If we draw an odd number, we win $13, and if we draw an even number, we win $0. Therefore, the expected payoff is:
(1/2) × $13 + (1/2) × $0 = $6.50
So on average, we can expect to win $6.50 per game if we play this game many times.
What is the value of 3¹. 34
The value of the expression is 243
What are index forms?Index forms are simply described as mathematical forms that are used or the representation of numbers that are too large or in small sizes in more convenient forms.
These index forms are also termed;
Scientific notationsStandard formsExamples of index forms are;
a³, b², c²
From the information given, we have that;
3¹. 3⁴
Now, since they are of the same bases, add their exponent values
3⁵
Find the values, we get;
243
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whats the lateral surface area
The lateral surface area of the given prism is 275.5 mm².
The lateral surface area of a prism is the surface area of the prism excluding the top and the base.
For the given prism the lateral surface area can be calculated as:
Lateral Surface Area
= (7.5mm × 9.5mm) + (11mm × 9.5mm) + (10.5mm× 9.5mm)
= 71.25 mm² + 104.5 mm² + 99.75 mm²
= 275.5 mm²
Hence, the lateral surface area is 275.5 mm².
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A baking company has developed two new cookie recipes, however, they only have the resources to add one item to their product line. They decide to randomly sample three groups of 100 people to determine which cookie recipe, A or B, is preferred. The results are shown in the following table.
Recipe A Recipe B
Sample #1 29 71
Sample #2 38 62
Sample #3 24 76
A. Based on the collected data, which recipe should the baking company add to their product line? How confident should the company be in their decision? Explain your reasoning using complete sentences.
B. Using the mean of the data for Recipe A, approximately what percentage of people would you expect to prefer Recipe A over Recipe B?
A)
There is a significant difference between the two recipes.
B)
We would expect approximately 30% of people to prefer recipe A over recipe B.
We have,
A.
To determine which recipe the baking company should add to its product line, we can perform a hypothesis test.
The null hypothesis would be that there is no difference between the two recipes (i.e., the proportion of people who prefer recipe A is the same as the proportion who prefer recipe B), and the alternative hypothesis would be that there is a difference between the two recipes.
We can use a two-sample proportion test to test the hypothesis.
Using the given data, the proportion of people who preferred recipe A in sample 1 is 0.29, in sample 2 is 0.38, and in sample 3 is 0.24.
The overall proportion of people who preferred recipe A is the average of these proportions, which is (0.29 + 0.38 + 0.24)/3 = 0.30.
Similarly, the overall proportion of people who preferred recipe B is 1 - 0.30 = 0.70.
To perform the hypothesis test, we calculate the test statistic z as:
[tex](P_1 - P_2)/\sqrt{\hat{P}(1/n_1 + 1/n_2)[/tex]
where p1 and p2 are the proportions of people who preferred recipe A in the two groups being compared, n1 and n2 are the sample sizes, and [tex]\hat{P}[/tex] is the overall proportion of people who preferred recipe A.
The calculated z-value is -4.07, which corresponds to a p-value of less than 0.0001.
Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is a significant difference between the two recipes.
Based on the results of the hypothesis test, the baking company should add recipe B to their product line, as it was preferred by a higher proportion of people overall.
However, the company should be somewhat cautious in its decision, as there is a small chance (less than 0.05) that the difference in preference between the two recipes could have occurred by chance alone.
B.
The mean of the data for recipe A is the average proportion of people who preferred recipe A across the three samples, which we calculated to be 0.30.
This means that we would expect approximately 30% of people to prefer recipe A over recipe B.
Thus,
There is a significant difference between the two recipes.
We would expect approximately 30% of people to prefer recipe A over recipe B.
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The solution is : 200 people were in the sample.
We have,
given data:
In a sample 76 people or 38% voted the mayor to be prosecuted.
solution:
how many people were in that sample
if 38% = 76 people
therefore;
let
p = total number of people
76/p = 38/100
cross multiply both sides
38p = 7600
divide both sides by 38
38p /38 = 7600 /38
p = 200
the number of people in the sample original was 200.
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complete question:
In a sample, 76 people or 38% of the people in the sample said that the mayor should be prosecuted for misconduct. How many people were in the sample
HELP MEEE
Factor x2 + x − 20.
(x − 2)(x + 10)
(x + 2)(x − 10)
(x − 4)(x + 5)
(x + 4)(x − 5)
Answer:
C, (x-4)(x+5)
Step-by-step explanation:
when u simplify the equetion (x-4)(x+5)
we get x2 + z +20
Answer:
[tex](x-4)(x+5)=x^2+x-20[/tex]
Step-by-step explanation:
[tex](x*x)+(x*5)+(-4*x)+(-4*5)=x^2+5x+-4x+-20[/tex]
[tex]x^2+5x+-4x+-20=x^2+(5-4)x-20[/tex]
[tex]x^2+(5-4)x-20=x^2+x-20[/tex]
What is the surface area?
Answer: 132.58312395178 cm^2 would be your answer!
Step-by-step explanation: I hope this helps!