Translate the sentence into an equation.
Five times the sum of a number and 9 equals 3.
Use the variable y for the unknown number.
Answer: To translate the given sentence into an equation, we can start by replacing the words "five times the sum" with the mathematical expression "5(x + 9)". Then, we can replace the word "number" with the variable y, to get:
5(y + 9) = 3
Next, we can distribute the 5 to obtain:
5y + 45 = 3
Finally, we can subtract 45 from both sides to solve for y:
5y = -42
y = -42/5
y = -8.4
Therefore, the equation that represents the given sentence is y = -8.4.
Step-by-step explanation:
A project requires you to figure out the area of a triangular lot. You take measurements and find that the lot has a base of 32 ft., while the altitude of the triangle, or height is 24 ft. What's the area of this lot?
Allen needs to prepare a compound for the patient to pick up tomorrow. He needs to mix 2/5 of drug A, with 5/3 of drug B and 9/3 of drug C. What is the total amount of the drugs mixed together?
Answer:
76/15 or 5 1/15
Step-by-step explanation:
2/5=6/15
5/3=25/15
9/3=45/15
6/15+25/15+45/15=76/15 or 5 1/15
The O'Neil family is taking a road trip. Their final destination is more than 243 miles from their house, and so far they have traveled 157 miles. Their
car can travel 21.5 miles on a gallon of gas. Which number line shows the solution set for the number of gallons of gas the O'Neil family needs to
reach their destination?
Answer:
The solution you are looking for is D.)
Step-by-step explanation:
To determine this, we need to find the amount of miles left they need to travel (243 - 157 = 86). Then we can divide that by the amount of miles per gallon (86 / 21.5 = 4). Because a possible solution to the answer is 4, we know that the dot needs to be solid (filled in), and because the solution can be greater than four, the arrow would be directed to the right / positive side of the line.
Can y’all pls help me solve this!!
Answer:
From left to right picture,
Scale factor = 2/3
x = 24
y = 12
z = 21
Step-by-step explanation:
Look at the two figures and identify the sides where both lengths are known.
That is the top right-hand side.
Scale factor is hence 18/27 = 2/3
Next, find x, y and z:
Bottom left-hand side: 16/x = 2/3
x = 3/2 x 16
x = 24
Bottom right-hand side: y/18 = 2/3
y = 18 x 2/3
y = 12
Top left-hand side: 14/z = 2/3
z = 3/2 x 14
z = 21
The scores of fourth grade students on a mathematics achievement test follow a normal distribution with a mean of 75 and standard deviation of 4.
a) What is the probability that a single student randomly chosen form all those taking the test scores 80 or higher?
b) What is the probability that the sample mean score of 64 randomly selected student is 80 or higher?
c) What is the probability the sample mean score of 64 randomly selected students is between 74 and 76?
Answer:
The appropriate solution is:
(a) 0.1056
(b) 0
(c) 0.9544
Step-by-step explanation:
The given values are:
Mean,
[tex]\mu = 75[/tex]
Standard deviation,
[tex]\sigma = 4[/tex]
(a)
⇒ [tex]P(x>80)=1-(x<80)[/tex]
[tex]=1-P[\frac{x-\mu}{\sigma} <\frac{80-75}{4} ][/tex]
[tex]=1-P[\frac{x-\mu}{\sigma} <\frac{5}{4} ][/tex]
[tex]=1-P(z<1.25)[/tex]
By using the table, we get
[tex]=1-0.8944[/tex]
[tex]=0.1056[/tex]
(b)
According to the question, the values are:
[tex]n[/tex] = 64
[tex]\mu_\bar{x}[/tex] = 75
Now,
⇒ [tex]\sigma_\bar{x}[/tex] = [tex]\frac{\sigma}{\sqrt{n} }[/tex]
= [tex]\frac{4}{\sqrt{64} }[/tex]
= [tex]\frac{4}{8}[/tex]
= [tex]0.5[/tex]
⇒ [tex]P(\bar {x} >80 ) = 1 - P(\bar x <80 )[/tex]
[tex]=1 - P[\frac{(\bar x-\mu_\bar x)}{\sigma \bar x} < \frac{80-75}{0.5} ][/tex]
[tex]=1-P(z<10)[/tex]
By using the table, we get
[tex]=1-1[/tex]
[tex]=0[/tex]
(c)
As we know,
⇒ [tex]\sigma_\bar x[/tex] = [tex]\frac{\sigma}{\sqrt{n} }[/tex]
= [tex]\frac{4}{\sqrt{64} }[/tex]
= [tex]\frac{4}{8}[/tex]
= [tex]0.5[/tex]
then,
= [tex]P(74< \bar x <76)[/tex]
= [tex]P[\frac{74-75}{0.5} < \frac{\bar x-\mu \bar x}{\sigma \bar x} < \frac{76-75}{0.5} ][/tex]
= [tex]P(-2<z<2)[/tex]
= [tex]P(z<2)-P(z<-2)[/tex]
By using the table, we get
= [tex]0.9772-0.0228[/tex]
= [tex]0.9544[/tex]
Can someone pls help answer this asap!! I’d really appreciate it!
Answer:
124 degrees
Step-by-step explanation:
Since they are congruent the corresponding angles will be equal. There is only one obtuse in each triangle, Angles Y and N. N is measured to be 124 degrees so Y is also 124 degrees.
the ratio of students to adults at the open house is 9:7 suppose there are 832 students and adults at the open house. how many students are there
Answer:
To determine the number of students at the open house, you can use the fact that the ratio of students to adults is 9:7 and set up the following proportion:
students/adults = 9/7
You can then cross-multiply to find the value of "students":
7 * students = 9 * adults
7 * students = 9 * (832/(9+7))
7 * students = 832
students = 832 / 7
students = approximately 118.85714285714 students
To determine the number of students at the open house, you can use the fact that the ratio of students to adults is 9:7 and set up the following proportion:
Copy code
students/adults = 9/7
You can then cross-multiply to find the value of "students":
Copy code
7 * students = 9 * adults
7 * students = 9 * (832/(9+7))
7 * students = 832
students = 832 / 7
students = approximately 118.85714285714 students
Since the number of students must be an integer, the number of students at the open house is approximately 118 students.
Step-by-step explanation:
The midpoint of \overline{\text{AB}} AB is M(7, -7)M(7,−7). If the coordinates of AA are (8, -6)(8,−6), what are the coordinates of BB?
Using the formula for the midpoint of the line with given points A and B as the end points of the line, the coordinates of the point B is (6,-8).
How do you find the midpoint of a line segment?To find the midpoint of a line segment, you must first find the coordinates of the two endpoints of the segment. Then, take the average of the x-coordinates and the y-coordinates to find the x and y coordinates of the midpoint. This can be done by adding the x-coordinates and y-coordinates of the two endpoints together and then dividing by 2.
What is the formula for finding the midpoint of a line segment?
The formula for finding the midpoint of a line segment is:
Midpoint = ( (x1+x2)/2 , (y1+y2)/2 )
Where (x1,y1) and (x2,y2) are the coordinates of the two endpoints of the line segment.
Using the given coordinates of point A(8,-6) and the midpoint M(7,-7) of the line, and using the midpoint formula for a line AB,
Midpoint(M) = [tex](\frac{x1+x2}{2},\frac{y1+y2}{2} )[/tex]
where x1, y1 are coordinates of point A , and x2, y2 are the coordinates of point B
so , (7,-7) = [tex](\frac{8+x2}{2} , \frac{-6+y2}{2})[/tex]
equating the corresponding points,
7 =(8+x2)/2
therefore, x2 = 6
and , -7 = (-6+y2)/2
therefore , y2 = -8
Hence the coordinates of B is , (x2,y2 ) = (6,-8)
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Find the slope of the line passing through each of the following pairs of points. (–7, 1) (7, 8)
Answer:
1/2
Step-by-step explanation:
Slope(m)
= (y2 - y1)/(x2 - x1)
= (8 - 1)/(7+7)
= 7/14
= 1/2
Constant of Variation
Find the y-intercepts of the graph y = 10/x² ?
a. There are no y-intercepts
b. y-intercept is (0,1)
c. y-intercept is (0,2)
d. y-intercept is (0,3)
Please select the best answer from the choices provided
Answer:
A. There are no y-intercepts
Step-by-step explanation:
I calculated it logically
Solve by factoring
-3x^2-11x+2=0
Answer:
x = -11, 2/3
Step-by-step explanation:
-3x^2-11x+2=0
-(3x^2+11x-2) = 0
3x^2 + 11x - 2 = 0
3x^2 + 33x - 22x - 2 = 0 ==> 33-22=11 and 33/11=3 and -22/11=-2
3x(x + 11) - 2(x + 11) = 0 ==> factor
(3x - 2)(x + 11) = 0
3x - 2 = 0 x + 11 = 0
3x = 2 x + 11 - 11 = 0 - 11
{ x = 2/3 x = -11 } ==> x = -11, 2/3
I will give branliest! My problem is NUHUHH
Step-by-step explanation:
Ok so basically you have to do
a A' (1, 1), B' (3, 9), C' (9, 3)
b A' (-1, -1), B' (-1, -3), C' (-3, -3)
c A' (3, 3), B' (9, 3), C' (3, 9)
d A' (3, 3), B' (3, 9), C' (9, 3)
Answer:
c is incorrect
Step-by-step explanation:
There is 42,000 litres of water in the lake this year. Find the water in the lake, a year ago if the
water of the lake is decreased by 30% every year.
Answer:
60,000 liters
Step-by-step explanation:
30% of 60000 = 18000
60000 - 18000 = 42000
A study selected independent random samples of 50 dogs and 60 cats and found that 38 of the dogs and 15 of the cats could be trained to fetch a ball.
Do these data provide convincing evidence that the proportion of all dogs that can be trained to fetch a ball is greater than the proportion of all cats that can be trained to fetch a ball?
Use Alpha = 0.05.
Select all statements that are correct.
We have two independent random samples.
We have two groups in a randomized comparative experiment.
The 10% condition is met.
The 10% condition does not apply.
The expected number of successes and failures for both samples are 38, 12, 15, 45.
The expected number of successes and failures for both samples are 24, 26, 29, 31.
Answer:
Sorry for answering this late, only just found this.
Answers are
a. We have two independent random samples.
c. The 10% condition is met.
f. The expected number of successes and failures for both samples are 24, 26, 29, 31.
Step-by-step explanation:
EDGE 2021
Once I finish the assignment I'll be making a quizlet with the answers.
Jimmy bought one seedless watermelon
for $2. How many watermelons can
DeShawn buy if he has $6?
Answer:
3 watermelons
Step-by-step explanation:
So this is a basic unit rate problem, so you're going to divide:
6 ÷ 2 = 3
So DeShawn can buy 3 watermelons with $6
hope this helps:)
y= 2x + 7 (List 4 Ordered Pairs for the equation) 1 points each
Answer:
(1,9), (2,11), (3,13) (4,15)
Step-by-step explanation:
When u plug in those numbers for your x values, you get those numbers for the y values.
Which of the following is the correct equation for the trend line in the scatter plot?
The equation of the trend line will be : Y = (1/4)x - 1.
What is trend line in scatter plots?A trend line is a straight line that best represents the points on a scatterplot. The trend line may go through some points but need not go through them all.Given is a scatter plot a shown in the image.
The general equation of a straight line is -
y = mx + c
{m} - slope
{c} - intercept along the y - axis
We can find the slope as follows. The line passes through the points -
(4, 0) and (0, - 1). We can write -
m = (- 1 - 0)/(0 - 4)
m = - 1/-4
m = 1/4
and
[c] = - 1
So the equation of the trend line will be -
Y = (1/4)x - 1
Therefore, the equation of the trend line will be : Y = (1/4)x - 1.
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་་བ་ཆེ། འོན་ཏེ་ ས་གནས་ཀྱི འན
རས་ན། ན་ནས། ན་བ་ བས་ ཆུ་
Answer:
???
Step-by-step explanation:
How many ways can someone purchase at least one CD from a group of 5
rock, 3 metal, and 7 punk CDs?
Answer:
Step-by-step explanation:
Heavy metal (or simply metal) is a genre of rock music that developed in the late 1960s and early 1970s, largely in the United Kingdom and the United States.
Need help plz need to turn in before 12?!?!?!
Answer:
C = π (4yd)
C = 12.6yd
Step-by-step explanation:
If 2^2x=2^3, what is the value of x?
Answer:
B) 3/2
Step-by-step explanation:
Jonah bought 36-ounce Big Mouth soda. After he drinks 27 ounces what percent of his soda is left?
Six different students went to a used book sale. They recorded the prices of the books that they bought and created the dot plots below. Each X represents 1 book. Which of the following dot plots report a purchase of 8 books? Select all that apply.
Answer:
Options 3, 4, and 5
Step-by-step explanation:
just count the x's.
If it equals 8, then its correct
Find the volume of a cube that has a taotal surface area of 96 squares feet.
A.) 84.0ft³
B.) 84.06ft
C.) 84.06ft³
D.) 84.06ft^2
A model of a railroad car has a Scale Ratio of 1:87.1. If the model railroad car is 1.4 in high, how
tall is the actual railroad car?
Please answer this for me quick it’s due on Monday for me!!!
Answer:
The scale ratio of 1:87.1 means that for every 1 unit of measurement on the model (in this case, inches), there are 87.1 units of measurement on the actual railroad car. This means that the actual railroad car is 87.1 times larger than the model in every dimension. If the model is 1.4 inches tall, the actual railroad car would be 1.4 x 87.1 = <<1.4*87.1=122.54>>122.54 inches tall.
BRAINLIST! Please help
In the right triangle ABC with altitude BD on hypotenuse AC, the length of AC is 40.
what is triangle ?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric forms. The name given to a triangle with the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. Triangle angles add up to 180 degrees when combined together.
given
Use similar triangles,
BAC and DAB are similar
therefore
CA/AB = BA/AD
CA/20 = 20/10
cross multiply
AC = CA = 20*20/10 = 40
Or use metric relations
CA*AD = BA^2
CA = BA^2/AD = 20^2/10 = 40
In the right triangle ABC with altitude BD on hypotenuse AC, the length of AC is 40.
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I know it says college level, but it isn't lol.
A stew recipe uses 3 teaspoons of salt for every 4 cups of water.
Complete the table to show the relationship between the amounts of salt and water in the stew recipe. Enter a number in each box.
Can someone please help me quickly!! And also let me know if I got the first 2 correct
The amount of salt in 3/4 tablespoons is four times that of 3 tablespoons.
What is the amount of salt?A stew recipe uses 3 teaspoons of salt for every 4 cups of water.
There is a ratio issue here.
As X is to three, 3 is to 4.
3 : 4 :: X : 3
To eliminate the fractions, multiply each integer in the ratio by 12.
9 : 12 :: 9X : 12
This is a portion of what is
9 / 12 = 9X / 12
to obtain, cross-multiply.
9 / 12 = 3 teaspoons of salt,
Check: 3 cup of flour yields 3 cups, which is a 4x increase.
The amount of salt in 9/12 tablespoons is four times that of 3 tablespoons.
The amount of salt in 3/4 tablespoons is four times that of 3 tablespoons.
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