there are 100 1/5s in 20
Rodney thinks that sqaure to the third power of 64 is greater than 17/4. Sam thinks that 17/4 is greater. Who is right and why?
The result of a square to the third power is a number that mutiplied 3 times by itself results in the number inside the square.
For example
[tex]\sqrt[3]{8}=2[/tex]because 2*2*2=8.
In this case:
[tex]\sqrt[3]{64}=4[/tex]That is because 4*4*4=64.
Now, we compare this with 17/4:
[tex]\frac{17}{4}=4.25[/tex]Thus, since 4 is less than 17/4. The one who is right is Sam, because 17/4 is greater than 4
Mia has $238.12 deducted from his monthly pay for group health insurance. His employer pays 85% of the cost. What is the annual premium?
$238.12
$238.12 -------------------------- 15%
x -------------------------100%
x = (100 x 238.12) / 15
x = 23812/15
x = $1587.5
Annual premium = 1587.5 x 12
= $19050
What is the length of the longer post's shadow? Write your answer in a COMPLETE SENTENCE.
Given
The length of two vertical post is 2meters and 0.45 meter respectively.
And, the length of shadow of the shorter post is 0.85meter.
To find:
The length of the shadow of the longer post.
Explanation:
It is given that,
The length of two vertical post is 2meters and 0.45 meter respectively.
And, the length of shadow of the shorter post is 0.85meter.
That implies,
Then,
[tex]\begin{gathered} \frac{2}{0.45}=\frac{x}{0.85} \\ x=\frac{2\times0.85}{0.45} \\ x=\frac{1.7}{0.45} \\ x=3.78m \end{gathered}[/tex]Hence, the length of the shadow of the longer post is 3.78m.
Find the number of complex roots and the number of possible real roots for the equation: 2x^4-3x^3+x^2-7x+3=0
You have the following polynomial:
2x⁴ - 3x³ + x² + 7x + 3 = 0
Based on the grade of the previous polynomial, you can conclude that there are 4 roots.
The complex roots are always present in pairs. Then, it's possible the given polynomial has 4 complex roots. In case there are 2 real roots, then, there are two comlpex roots.
Otherwise, there are 4 real roots.
Then, you can conclude for the possible roots of the polynomial:
- 4 real roots
- 4 complex roots
- 2 real roots and 2 complex roots
Suppose you were given $600 from your uncle. You deposited that money in a bank and added $50 per month.
The 1-variable equation that we need to solve to find how many months it would take to save $10,000 is given when we equal s(x)=10,000.
Hence, the answer is:
[tex]50m+600=10,000[/tex]Now, to find how many months it would take to save 10,000, we need to solve for m the previous equation. Therefore:
[tex]50m+600=10,000[/tex]Subtract both sides 600
[tex]50m+600-600=10,000-600[/tex][tex]50m=9400[/tex]Then, divide both sides by 50:
[tex]\frac{50m}{50}=\frac{9400}{50}[/tex][tex]m=188[/tex]Hence, it would take 188 months to save $10,000
On the grid below triangle MNP is plotted with vertices at M(-10,-2), N(-6,-9) and P(1,-5). The line y=-2/3x is also drawn.(a) Draw the image of triangle MNP after a reflection in y=-2/3x. Give the coordinates of the transformed vertices below.(b) Explain why triangle M'N'P' must have the same area as triangle MNP.
We have the following:
The reflection is:
[tex]\begin{gathered} M(-10,-2)\rightarrow M^{\prime}(2,10) \\ N(-6,-9)\rightarrow N^{\prime}(9,6) \\ P(1,-5)\rightarrow P^{\prime}(5,-1) \end{gathered}[/tex]a) The graph is:
b)
Since the sides are still the same length, for this reason keep the same area
The distance between two cities on a map is 25 inches. The actual distance between the two cities is 500 miles. How many miles would 35 inches be on the map?
1.75 miles
20 miles
510 miles
700 miles
35 inches on the map will translate to an actual distance of 700 miles (fourth option).
What is the distance in miles?The first step is to determine the scale of the map. In order to determine the scale, divide the actual distance between the two cities by the distance on the map.
Scale = distance between the two cities / distance on the map
Scale = 500 / 25 = 20
Now, multiply the distance on the map by the scale.
Distance in miles = 20 x 35 = 700 miles
To learn more about scale drawings, please check: https://brainly.com/question/26388230
#SPJ1
Answer:
35 inches on the map will translate to an actual distance of 700 miles (fourth option).What is the distance in miles?The first step is to determine the scale of the map. In order to determine the scale, divide the actual distance between the two cities by the distance on the map. Scale = distance between the two cities / distance on the map Scale = 500 / 25 = 20 Now, multiply the distance on the map by the scale. Distance in miles = 20 x 35 = 700 milesTo learn more about scale drawings, please check: brainly.com/question/26388230#SPJ1
Step-by-step explanation:
I need help with a graph in question (To graph the point (5,2))
To graph a point in the cartesian plane you can use rectangular coordinates. These coordinates (in a 2D plane) are given by values of x and y:
So if you want to graph a point, let's say (a,b). You must move "a" steps to the right and "b" steps upwards.
In your exercise, you have to graph the point (5,2), therefore you have to move "5" steps to right and "2" steps upwards:
i was absent for the day we reviewed the question and my teacher won't help me understand. the image given is my problem.
Step 1. Find the coordinates of point D.
In this problem, we have a segment called CD with two endpoints. We know one of the endpoints:
[tex](2,-1)[/tex]And we don't know the other endpoint, but we know the midpoint:
[tex](8,3)[/tex]We will label these known points as the first point (x1,y1) and the midpoint (xm, ym) as follows:
[tex]\begin{gathered} x_1=2 \\ y_1=-1 \\ x_m=8 \\ y_m=3 \end{gathered}[/tex]To find the second endpoint which we will call the second point (x2,y2) we use the midpoint formulas:
[tex]\begin{gathered} x_m=\frac{x_1+x_2}{2} \\ y_m=\frac{y_2+y_2}{2} \end{gathered}[/tex]Solving each equation respectively for x2 and y2:
[tex]\begin{gathered} x_2=2x_m-x_1 \\ y_2=2y_m-y_1 \end{gathered}[/tex]And substituting the known values for the first point and the midpoint:
[tex]\begin{gathered} x_2=2(8)-2=16-2=14 \\ y_2=2(3)-(-1)=6+1=7 \end{gathered}[/tex]We have found the second endpoint (x2,y2):
[tex](14,7)[/tex]Step 2. Once we know the two endpoints of the segment CD:
[tex]\begin{gathered} (2,-1) \\ \text{and} \\ (14,7) \end{gathered}[/tex]We make a graph for reference:
Note: the diagram is not to scale.
The length of the red line is what we are asked to find.
To find this length, draw a triangle between the points, shown here in green:
The triangle is a right triangle, this means we can use the Pythagorean theorem:
The Pythagorean theorem helps us find the hypotenuse ''x'' of the triangle when we know the legs a and b.
In this case, a and b are:
Substituting in the Pythagorean theorem:
[tex]\begin{gathered} x=\sqrt[\square]{a^2+b^2} \\ x=\sqrt[]{12^2+8^2} \end{gathered}[/tex]Solving the operations:
[tex]\begin{gathered} x=\sqrt[]{144-64} \\ x=\sqrt[]{80} \\ x=8.9 \end{gathered}[/tex]The solution is b. 8.9 units.
Answer: 8.9 units
If three times the sum of a number and 1 is 15, find the number.
The number is 4.6
Let the number be x
The equation will be 3x+1=15
on solving the equation we get
3x = 15-1
X = 14/3
X = 4.6
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Use the Pythagorean theorem to find each missing length to the nearest tenth I want you tell how to do please
Let the unknown side be h
Pythagoras theorem states that the square of the hypotenuse is equal to the square of the opposite plus the square of the adjacent in any right angled triangle
[tex]\begin{gathered} \text{From the figure, } \\ \text{hypotenus = h} \\ \text{Let opposite = 3, adjacent = 10} \\ \text{Therefore, applying pythagoras theorem,} \\ h^2=3^2+10^2 \\ h^2=9+100 \\ h^2=109 \\ h=\sqrt[]{109} \\ h=10.44 \\ h\approx10.4\text{ (nearest tenth)} \end{gathered}[/tex]The missing length is 10.4
if i can't do the practice test how am I gonna pass the actual test lol
According to the given diagram, angles COD and DOE are complementary angles because they are on a right triangle, which means they sum 90°.
[tex]\begin{gathered} m\angle COD+m\angle DOE=90 \\ 54+m\angle DOE=90 \\ m\angle DOE=90-54 \\ m\angle DOE=36 \end{gathered}[/tex]Therefore, angle DOE is 36°.Question 3 The graph of the equation x + 3y=6 intersects the y- axis at which coordinate point? (0, 2) (0, 6) (0, 18) (6, 0)
The intersection with the y-axis ocurrs at x=0. That is, by substituting x=0 in our given expression, we get
[tex]0+3y=6[/tex]which gives
[tex]\begin{gathered} 3y=6 \\ y=\frac{6}{3} \\ y=2 \end{gathered}[/tex]Then, the intersection point is (0,2). Which corresponds to the first option.
In an all boys school, the heights of the student body are normally distributed with a mean of 71 inches and a standard deviation of 3.5 inches. Out of the 1707 boys who go to that school, how many would be expected to be taller than 75 inches tall, to the nearest whole number?
The formula for the z score of a number is given by:
[tex]z=\frac{x-\overline{x}}{\sigma}[/tex]Where:
[tex]\begin{gathered} x=\text{ the observed value} \\ \overline{x}=\text{ the mean} \\ \sigma=\text{ the standard deviation} \end{gathered}[/tex]In this case,
[tex]\begin{gathered} x=75 \\ \overline{x}=71 \\ \sigma=\text{ 3.5} \end{gathered}[/tex]Therefore, the z score of x=75 is given by:
[tex]z=\frac{75-71}{3.5}=\frac{4}{3.5}\approx1.143[/tex]Therefore, the probability that a boy is taller than 75 inches is given by the area under the normal probability distribution curve between z=1.143 and z=∞, P(z > 1.143):
The area is approximately 0.1265.
Therefore, the required probability is 0.1265.
Convert the probability to percent by multiplying with 100:
[tex]0.1265\times100=12.65[/tex]Hence, about 12.65 % of all the boys are taller than 75 inches.
Therefore, the total number of boys that are taller than 75 inches is given by:
[tex]\frac{12.65}{100}\times1707\approx216[/tex]Therefore, the number of boys expected to be taller than 75 inches is approximately:
216
Sallys recipe for chocolate chip cookies yields 48, 1 oz cookies. If she want to make 48,2 oz cookies what is her conversation factor??(Hint : how many total oz cookies is in the original recipe yield and the new recipe yields)
Please help and show me how you got it as best as possible step by step im struggling and need to show my work
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the formula for area of a rectangle
[tex]Area=length\times width[/tex]STEP 2: Write the given measure of the sides
[tex]\begin{gathered} length=3x+2 \\ width=2x-1 \end{gathered}[/tex]STEP 3: Calculate the area
By substitution,
[tex]\begin{gathered} Area=(3x+2)(2x-1) \\ \mathrm{Apply\:FOIL\:method}:\quad \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd \\ \left(3x+2\right)\left(2x-1\right)=3x\cdot \:2x+3x\left(-1\right)+2\cdot \:2x+2\left(-1\right) \\ =3x\cdot \:2x+3x\left(-1\right)+2\cdot \:2x+2\left(-1\right) \\ =6x^2+x-2 \end{gathered}[/tex]Hence, the area of the rectangle is
[tex]6x^2+x-2[/tex]the following data set shows the number of books checked out from the library during the first two weeks of the month .36, 39, 40, 42, 45, 2, 38, 41, 37, 38, 35, 37, 35, 38
According to the given data set, we can observe that there's one day where people only checked out 2 books which is way too low compared to the other days, which represents an outlier.
Hence, the answer is 1) there is one outlier, indicating very few books were checked out on that day.please help me figure out how to determine the range of the following graph (the line y=5 is a horizontal asymptote)
we are given the graph of the function and we are interested in finding the range of the function. Recall that the range of a graph is simply the set of values on the y axis, for which there is a point on the graph that has that y coordinate.
One easy way to spot this set, is by taking any point on the graph and then drawing a horizontal line. Wherever the line crosses the y axis, that point is included in the range.
From the graph, we can see that no part of the graph has values with y coordinate less than 5. That is, any number less than 5 in the y coordinate would indicate that there is no point on the graph at that "height". So every number less than 5 is excluded from the range.
We are also told that line y=5 is a horizontal asymptote. This means that despite the graph is really close to the line y=5 (and it keeps getting closer and closer as x increases), it never touches the line. This means that the point 5 is excluded from the range.
Finally, we can see that above the horizontal line y=5, if we draw a horizontal line on the graph, it will touch the y axis. This means that every number greater than 5 is part of the range. Then, the set of numbers that represent the range is
[tex](5,\text{infinity)}[/tex]identify the class in their frequency choose the correct answer below
Given the following question:
Identify the classes and their frequencies
Using the histogram we can find....
60-69 is 2
It wouldn't be option A because you can see the length of the bar is 60 - 70, - 80 - 90 etc...
The answer would be the third option where it gives a accurate descprition of the 7th graders IQ scores where it's rounded to the nearest whole number.
find three comsecutive even integers whose sum is 162. enter your answers as a coma -seperated list.
To answer this question we will set and solve an equation.
Let x, x+2, and x+4 be three consecutive even integers whose sum is 162, then we can set the following equation:
[tex]x+x+2+x+4=162.[/tex]Adding like terms we get:
[tex]3x+6=162.[/tex]Subtracting 6 from the above equation we get:
[tex]\begin{gathered} 3x+6-6=162-6, \\ 3x=156. \end{gathered}[/tex]Dividing the above equation by 3 we get:
[tex]\begin{gathered} \frac{3x}{3}=\frac{156}{3}, \\ x=52. \end{gathered}[/tex]Therefore the three consecutive even integers whose sum is 162 are:
[tex]52,54,56.[/tex]Answer:
[tex]52,54,56.[/tex]
Items 8-10. triangle DEF is shown below.8. What is measure DEF9.Select all the descriptions for segment GE.10. Select all the points that segment GE contains.
8.
ΔDEF is an isosceles triangle, therefore:
[tex]\begin{gathered} m\angle DEF=m\angle DEG+m\angle FEG \\ \text{where:} \\ m\angle DEG=3y+4 \\ m\angle FEG=5y-10 \\ m\angle DEG=m\angle FEG \\ 3y+4=5y-10 \\ \text{solving for y:} \\ 2y=14 \\ y=7 \\ m\angle DEG=m\angle FEG=3(7)+4=25 \\ m\angle DEF=25+25 \\ m\angle DEF=50 \end{gathered}[/tex]9.
C. Perpendicular bisector
A. Angle bisector
D. Altitude ( If your teacher mean height)
B. Median
10.
A. Circumcenter
B. Incenter
C. Orthocenter
D. Centroid
Choose the answer that best completes the visual analogy.62Х**is to.oOХo*asis to?
The question wants us to choose the answer that best completes the visual analogy.
Before we will choose, let's first of all know what visual analogy is is.
Visual analogies are use to determine graphical patterns.
Theses are the ways you can determine a complete image.
When the corresponding shapes are the same , then the transformed shape is a square.
When the corresponding shapes are not the same, the shape at the top top takes precedence over the shape st the bottom.
So, from the above illustrations, the answer that completes the analogy would be the Third image.
Focus (1,4)Directrix=x-7,What is the vertex (h,k)?what is p?what is the equation?
Let's begin by listing out the information given to us:
[tex]undefined[/tex]3. Create a fraction with a denominator of 100 that is equivalent to to Your answer DELL
80/100
Explanation:We are to find an equivalent fraction to 8/10. But in this case the denominator needs to be 100
[tex]\begin{gathered} \text{Given denominator = 10} \\ \text{new denominator = 100} \\ \frac{\text{new denominator }}{\text{given denominator }}=\frac{100}{10}=\text{ 10} \end{gathered}[/tex]This means the multiplying number to the given denominator is 10.
For equivalent fraction, we multiply the numerator and the denominator by the same number
So we would multiply the given numerator too by the multiplying number 10
[tex]\begin{gathered} \text{Given numerator = 8} \\ \text{New numerator = 8}\times10\text{ = 80} \end{gathered}[/tex]The equivalent fraction to 8/10 becomes:
[tex]\begin{gathered} Thefraction=\frac{\text{new numerator}}{\text{new denominator}} \\ Thefraction=\frac{80}{100} \end{gathered}[/tex]the results for a survey of 120 students were selected randomly are listed below
The percentage of students that have a cell phone plan with company Y is:
36 / 120 (total of the surveyed students) *100 = 30%
Then, we use that percentage with the total of the students (380)
30 % of 380
30/100*380
114 (Multiplying)
The answer is the option A.
Write each of the numbers one, four, nine, 16 and 25 as a base raise to the second power. Explain why these numbers sometimes are called “perfect squares”.BUT ONLY NUMER 5
In all the following cases you obtain the first number as result of the multiplication of the base of the base of the cond number by itself.
1 = 1²
4 = 2²
9 = 3²
16 = 4²
25 = 5²
Question 8 of 10, Step 1 of 15/10CorrectIn a park, the ratio of adults to children is 12 to 11. If there are 368 people in the park, how many children are there?AnswerекеKeyboard ShochildrenSubmit Answer
STEP - BY - STEP EXPLANATION
What to find?
Number of children in the park.
Given:
• Ratio of adult to children =12: 11
,• Total ratio =23
,• Number of people in the park =368
To solve the given problem, we will follow the steps below:
Step 1
Use the formula below to solve the given problem:
[tex]Number\text{ }of\text{ }children=\frac{ratio\text{ of children}}{total\text{ ratio}}\times number\text{ of people}[/tex]Step 2
Substitute the values into the formula.
[tex]Number\text{ }of\text{ }children=\frac{11}{23}\times368[/tex][tex]=\frac{4048}{23}[/tex][tex]=176[/tex]Therefore, there are 176 children in the park.
the following ordered pairs give the entrance exam scores x and the grade-point averages y after 1 year of college for 10 students.find the equation of a line that models entrance exam scores and GPA.
If this is a linear function between x and y, the slope will be constant.
We can pick any two ordered pairs, like (75, 2.3) and (82, 3) and calculate the slope as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-2.3}{82-75}=\frac{0.7}{7}=0.1[/tex]We can write the point-slope form of the equation and rearrange to find the value of the y-intercept and the slope-intercept form of the equation:
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-3=0.1(x-82) \\ y=0.1x-0.1\cdot82+3 \\ y=0.1x-8.2+3 \\ y=0.1x-5.2 \end{gathered}[/tex]We can test if the equation is correct with another point, like (65,2):
[tex]\begin{gathered} y=0.1x-5.2 \\ y(65)=0.1(65)-5.2 \\ y(65)=6.5-5.2 \\ y(65)=1.3 \end{gathered}[/tex]This is not a exact line, so we have to apply a regression model to find the approximate line that best represent this relationship:
Answer: the linear regression model that best represents the relation between x and y is y=0.0736x-3.0166.
You are asked to create a graphic that would make it easy to quickly tell which locations require that ear protection be worn after 12 hours of exposure with the understanding that the sound level limit is 87. Would the proposed new graphic accomplish this purpose?
Answer:
Step-by-step explanation:
The answer would be "Yes, because ordering from lowest sound level to highest sound level makes it easy to use the exposure graph to see what time is permitted."
Hopes this helps.
I need help with this I need to know what I’m doing wrong.. do I need to put a negative for (y+8^2) or a positive 8 so confused… help #4write in standard equation for a circle and identify center and radius
4) You have the following equation:
[tex]x^2+10x+y^2-16=0[/tex]In order to determine the radius and center of the circle, complete squares for x. You don't complete squares for y because there is no term with y in the given expression. It is only a y^2 term.
By adding 25 and subtracting 25 left side of the equation you obtain:
[tex]x^2+10x+25+y^2-16-25=0[/tex]The first three terms are a perfect square (x + 5)^2, then, by using this factor and by simplifying in the previous equation you can write:
[tex](x+5)^2+y^2-41=0[/tex]Finally, add 41 both sides:
[tex](x+5)^2+y^2=41[/tex]The previous equation is in standard form for a circle equation:
[tex](x-h)^2+(y-k)^2=r^2[/tex](h,k) is the center of the circle and r the radius. By comparin the previous equation with the expression you obtain you obtain:
center of the circle = (-5,0)
radius r = √41