Answer:40%
Step-by-step explanation: Take 16 divided by 40 and you get .04, which equals 40 percent. Another way to think about it is this way: if 40 miles is the total distance, every 4 miles is 10% of the total. So 16 has to be 40%.
a sample survey interviews an srs of 209 college women. suppose that 69% of all college women have been on a diet within the last 12 months. what is the probability that 72% or more of the women in the sample have been on a diet? report your answer using 4 decimal places.
The probability that 72% or more of the women in the sample have been on a diet is, 0.1736.
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.
As given a sample survey interviews an SRS of 209 college women. suppose that 69% of all college women have been on a diet within the last 12 months.
p = 0.69
1 - p = 0.31
n = 209
μp = p = 0.69
σp = √(p(1-p))/n = √(0.69*0.31)/209 = 0.03199
= 1 - p(p < 0.72)
= 1 - p((p - μp) / σp < (0.72 - 0.69) / 0.03199)
= 1 - p(z < 0.94)
= 1 - 0.8264
= 0.1736
Hence, the probability is 0.1736.
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There is one negative solution and two nonreal solutions to the equation x3 + 87 = 7x2 + x. What are the solutions?
3, 5 + 2i, 5 – 2i
3, –5 + 2i, –5 – 2i
–3, 5 + 2i, 5 – 2i
–3, –5 + 2i, –5 – 2i
The solutions to the expression x³ + 87 = 7x² + x are given as follows:
–3, 5 + 2i, 5 – 2i.
How to obtain the solutions to the equation?The equation is defined as follows:
x³ + 87 = 7x² + x.
In standard format, it is given by:
x³ - 7x² - x + 87 = 0.
It has one negative solution, hence from the options it is:
x = -3.
The verification is:
(-3)³ - 7(3)² - (-3) + 87 = 0.
Considering the linear factor (x + 3), the function can be written as follows:
x³ - 7x² - x + 87 = (x + 3)(ax² + bx + c).
As the product of a linear function and a quadratic function results in a cubic function.
Expanding the right side of the equality, we have that:
ax³ + (b + 3a)x² + (3b + c)x + 3c = x³ - 7x² - x + 87.
Hence the coefficients of the quadratic equation are given as follows:
a = 1.b + 3a = -7 -> b = -10.c = 87/3 = 29.Hence the equation is:
x² - 10x + 29 = 0.
And the solutions, using a quadratic equation calculator, are given as follows:
x = 5 + 2i.x = 5 - 2i.Which means that the third option is correct.
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How much would you subtract from the grouping?
(4 – 2)4 – 42 × 4
Answer:
-160 I think so
Step-by-step explanation:
(2)4-168
8-168
-160
Which of the following is NOT a solution to -4x + 9 > -3
A: -3
B: -1
C: 3
D:5
Answer:
D
Step-by-step explanation:
-4x + 9 ≥ -3 Subtract 9 from both sides
-4x ≥ -12 Divide both sides by -4. When you divide both sides by a negative number, you must flip the inequality sign.
x ≤ 3
D: 5 is not a solution.
Answer:
D) 5
Step-by-step explanation:
To solve this problem, we must first isolate the variable and simplify the inequality. Isolating the variable means having the variable on one side of an equation or inequality without any other terms?
How do you isolate a variable?
Here's an example.
x+3=18
What can we do to have x on its own side of the equation? Currently, 3 is also with it. If we subtract 3 on both sides, we are leaving the equation with the same answer.
x + 3 - 3= 18 - 3
Combine like terms.
x = 21
That's how you solve for an equation.
Next, an example with division.
3x = 21
How do we solve for x this? Well, we know that 3x = 3 times x. So, to solve for x, we remove the 3. Since its 3 times x, lets divide by 3 on both sides.
[tex]\frac{3x}{3} =\frac{21} {3}[/tex]
Simplify:
3x/3 means 3 times x divided by 3. 3/3 = 1
1x = 21/3
21/3 = 7
x = 7
Now lets get to the problem.
[tex]-4x + 9 \geq -3[/tex]
The first step is to subtract by 9 on both sides so we can work our way to isolating the variable and solving the problem.
[tex]-4x + 9 -9\geq -3 - 9[/tex]
Simplify.
[tex]-4x \geq -12[/tex][tex]-4x \geq -12[/tex]
Now heres the tricky part. To solve for an equation, we must remove -4 from x, or -4 times x. In an equality, which states that:
A [tex]\geq , \leq , > , or < B[/tex]
If you divide or multiply both sides by a negative number, which means the number is less than 0, you must flip the sign!
When you multiply/divide by a negative number or both sides in an equality:
[tex]\leq[/tex] [tex]\geq[/tex]
[tex]\geq[/tex] [tex]\leq[/tex]
> <
< >
So, we currently have:
[tex]-4x \geq -12[/tex]
Divide by -4 on both sides.
[tex]\frac{-4x}{-4} \geq \frac{-12}{-4}[/tex]
Simplify. (Use the rule which states that a negative number multiplied or divided by another negative number equates to a positive number).
[tex]x \geq 3[/tex]
Flip the sign (This is a crucial step!)
[tex]x \leq 3[/tex]
Now, [tex]x \leq 3[/tex] means any number equal to or lower than 3 satisfies the conditions of the inequality.
Is -3 lower than or equal to 3?
Yes; Lower
Is -1 lower than or equal to 3?
Yes;
Is 3 lower than or equal to 3?
Yes; Equal
Is 5 lower than or equal to 3?
No; Greater
D, 5 is your answer as it does not satisfy the inequality.
Use the Law of Detachment to draw a conclusion from the two given statements.
If two angles are complementary, then the sum of their measures is 90°.
The Law of detachment states that if m then n and m is true then q is true.
If two angles are complementary, then the two angles' sum is 90 degrees.
This is m∠E + m∠F = 90.
Option C is the correct answer
What is the law of detachment?The Law of detachment states that if m then n and m is true then q is true.
We have,
If two angles are complementary, then the sum of their measures is 90°.
This is in the form of,
If M then N and if M is true then N must be true.
So,
If two angles are complementary, then the two angles' sum is 90 degrees.
If the two angles are m∠E and m∠F.
m∠E + m∠F = 90
Thus,
If two angles are complementary, then the two angles' sum is 90 degrees.
This is m∠E + m∠F = 90.
Option C is the correct answer
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What is the converse of the conditional statement "If the streetlights are on, then the sun has gone down."?
O If the sun has gone down, then the street lights are on.
O If the streetlights are not on, then the sun has gone down.
O If the streetlights are not on, then the sun has not gone down.
If the sun has not gone down, then the streetlights are on.
The converse of the conditional statement "If the streetlights are on, then the sun has gone down" is If the sun has not gone down, then the streetlights are on and is denoted as option D.
What is Converse of the conditional statement?This is referred to as the type of sentence which is formed when the hypothesis and the conclusion are interchanged.
In this scenario, "If the streetlights are on, then the sun has gone down" when interchanged will be If the sun has not gone down, then the streetlights are on which therefore makes option D the correct choice.
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Erin wants to buy a dictionary that costs $12, a dinosaur book that costs $16, and a
children's cookbook that costs $11. She has saved $29 from her allowance. How much
more money does Erin need to buy all three books?
Answer:
Erin would need $10 more dollars in order to buy all three books.
Step-by-step explanation:
Step one: find the cost of all books
12 +16 +11 = 39
Step two: subtract
39 -29 = 10
Step two: Get your Answer!
Erin would need $10 more dollars in order to buy all three books.
Find the component form of the vector that translates (3, − 2) to ′(− 1, 4)
The vector that translates P to P' is (-4 , 6)
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x).
The points are given;
[tex]{P = (3, -2)}\\{P' = (-1, 4)}[/tex]
The translation rule is calculated as:
{(x,y) = P' - P}
So, we have:
{(x,y) =(− 1, 4) - (3, − 2)}
Combine the terms;
{(x,y) = (-1 -3 , 4 + 2)}
{(x,y) = (-4 , 6)}
Express as vectors;
(x, y) = (-4 , 6)
Hence, the vector that translates P to P' is (-4 , 6)
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find the distance when r=55 mi/hr and t =3
The distance when r = 55 mi/hr and t = 3 hours is 165 miles .
In the question ,
it is given that ,
r = 55 mi/hr which means the speed is 55 mi /hr
t = 3 hours , which means time = 3 hours .
we need to find the distance when r=55 mi/hr and t =3 hours .
the formula to calculate the distance is written as
distance = Speed × time
Substituting the value of speed = 55 and time = 3 ,
we get ,
distance = 55 × 3
distance = 165 miles .
the distance is 165 miles .
Therefore , The distance when r = 55 mi/hr and t = 3 hours is 165 miles .
The given question is incomplete , the complete question is
Find the distance when r=55 mi/hr and t = 3 hours ?
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after begging his parents for 3 years, jason is finally going to clown college! on the first day, his juggling instructor divides a box of bean bags equally among the 16 clowns in jason's class. each clown gets 6 bean bags. which equation can you use to find the number of bean bags b in the instructor's box?
The equation that can be used to determine the number of bean bags in the instructor's box is b = 17 x 4.
Given,
In the question:
His juggling instructor divides a box of bean bags equally among the 16 clowns in Jason's class. each clown gets 6 bean bags.
Now, According to the question:
The equation that can be used to determine the number of bean bags in the instructor's box is b = 16 x 6.
The number of bean bags in the instructor's box is 96.
What is multiplication?
Multiplication is a mathematical operation that can be used to determine the product of two or more numbers. The sign used to represent multiplication is ×.
Hence, The equation that can be used to determine the number of bean bags in the instructor's box is b = 17 x 4.
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wer:
Find the slope of the line that passes through the given points.
(-3, 7.2) and (2,-2.3)
Answer:
Step-by-step explanation:
this slope of a line question is such a common question. I feel like math teachers all over don't understand how to teach this subject. Just so you know, I answer a question like this about 10 times a day when I am on here. It's like one of the most common questions.
Here is my copy and paste answer for this...
point P1 (-3,7.2) in the form (x1,y1)
point P2(2,-2.3) in the form (x2,y2)
slope = m
m = (y2-y1) / (x2-x1)
m = (-2.3-7.2) / (2-(-3))
notice all the minus signs and how i'm being very careful to keep close track of them. Also, who ever has written this question is intentionally trying to trip you up by putting in all the minus signs, there is no need for so many minus signs to teach this well. Anyway...
m = -8.5 / 5
m = - 1.7
the problem question ends there , but there is a common place this question is supposed to take you. to the point slope formula. but for another question.
The slope of (-3, 7.2) and (2, -2.3) is -1.9.
Consider,
(x1, y1) = (-3, 7.2)
(x2, y2) = (2, -2.3)
slope = (y2 - y1)/(x2-x1)
slope = ((-2.3) - (7.2))/((2) - (-3))
slope = (-9.5)/(5)
slope = -1.9
Therefore, the slope of the given points (-3, 7.2) and (2, -2.3) is -1.9.
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A movie theater has a seating capacity of 183. The theater charges $5.00 for children, $7.00 for students,
and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $
1316, How many children, students, and adults attended?
children attended.
Using simplification, if the total ticket sales was $1316, then 70 children, 78 students and 35 students attended.
From the given question,
We know that the capacity of movie theater is 183.
The theater charges $5.00 for children, $7.00 for students and $12.00 of adults.
There are half as many adults as there are children.
If the total ticket sales was $1316, then we have to find how many children, students, and adults attended.
Let the number of children that attended = x
Since, there are half as many adults as children.
Therefore number of adults = 1/2x =0.5x
We know there are total of 183 tickets
Therefore number of students = 183 - x - 0.5x
number of students = 183 - 1.5x
Each children ticket costs = $5
Then the price of children tickets = 5x
Similarly for adults each ticket costs = $12
So total cost of adult ticket = 12×0.5x = $6x
Now the cost of student tickets = 7(183 - 1.5x)
As given that
Total cost of all tickets = $1316
So the expression should be
5x + 6x + 7(183 -1.5x) = 1316
Simplifying
11x + 1281 - 10.5x = 1316
Subtract 1281 on both side
11x + 1281 - 10.5x-1281 = 1316-1281
Simplifying
0.5x = 35
Divide by 0.5 on both side we get
x = 70 children
Now finding the number of adults
= 0.5x
= 0.5×70
= 35 adults
Now finding the number of students
= 183 - 1.5x
= 183 - 1.5×70
= 183 - 105
= 78 students
Hence, If the total ticket sales was $1316, then 70 children, 78 students and 35 students attended.
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Today, Austin's age
is 1/4 of Stephanie's
age. In 4 years,
Austin's age will be
2/5 of Stephanie's age.
How old is Stephanie
today?
Answer: Steph is 16 today
Step-by-step explanation:
Austin age today = x
Austin in 4 years = x+4
Steph age today = 4x (because Austin is 1/4 her age today)
Steph age in 4 years is 4x + 4
In 4 years Austin's age is 2/5 of Steph's, so:
2/5 (x+4) = 4x + 4
Now solve for x!
x+4 = (8/5)x + 8/5
12/5 = (3/5)x
Therefore Austin is 4 years old today (x=4) and...
Steph age today = 4x = 4x4 = 16
In the formula A = r², find A when ris
14 centimeters.
Step-by-step explanation:
A = r², find A when r is 14 centimeters.
A = (14)²
A = 196 cm²
Two squares are similar. The
perimeter of the smaller square is p
46 cm. The perimeter of the larger
square is doubled the perimeter of
smaller square. Find the side
length (in cm) of the
larger square.
Answer:23
Step-by-step explanation:
Divide 46 by 4 so u know the length of the side of the smaller square
the answer is 11.5 so them you multiply It by 2 and you get 23cm
hope this helps
HELP HELP HELP
(2^4x+4) / (2^x+1)
Answer:
[tex]2^{3x+3}[/tex]
Step-by-step explanation:
to divide exponents with the same base you just subtract them
(4x+4)-(X+1)
4x+4-x-1
3x+3
Hopes this helps please mark brainliest
Answer:
frac{16x+4}{2^{x}+1 =
Step-by-step explanation:
Evaluate the exponent! hope this helped
A web designer charges a $200 fee plus $50 per hour to build a website. Which equation represents the total cost, y, to a customer based on the number of hours, x, it takes to buld the website?
Answer: 50x+200=y
Step-by-step explanation:
This is the answer because the number of hours is not provided leaving us to multiply 50 by x, 200 is the flat fee so we will know to automatically add that to our first step and since y is the total this will form the equation, 50x+200=y.
What is an equation of the line that passes through the point (3,-1)(3,−1) and is parallel to the line 5x+3y=6
Answer: y=-5/3x+4
Step-by-step explanation:
Since the line is parrallel that means that the gradient is the same
We can reorder 5x+3y=6 into 3y=-5x+6 but in order to find the gradient the number infront of y must be 1 so...
3y=-5x+6
y=-5/3x+2
Now we know that the gradient is -5/3
To find th y-intercept we just subsitute the points it passes through (3, -1) into the equation
y=-5/3x+c
-1=-5/3(3)+c
-1=-5+c
4=c
10. Which segment below is perpendicular to line AB? How do you know?
Answer:
Line CE
Step-by-step explanation:
We know that lines are perpendicular when their intersections form 90° angles (see below diagram). ∠E is a 90° angle, so line CE is perpendicular to line DF. Assuming that line DF is parallel to line AB, we now know that line CE is also perpendicular to line AB.
Please do the one you understand anything is helpful!
Answer:
1. 30 years old
2. 7 years old
3. 5 hours
Step-by-step explanation:
We can solve all of these problems using algebraic equations.
1. In this question, we will use variable x to represent the age of Mrs. Olsen's daughter.
In 10 years, x - 20 = 2x. That means that in 10 years, Mrs. Olsen will be 40 years old. That means she is 30 right now.
2. In this question, we will use variable x to represent the age of Alyssa.
If, in 30 years, their total age is 88, their current total is 28. Tyler is 3 times as old as Alyssa, so Tyler is 21 and Alyssa is 7.
3. Ryan leaves home at 50 mph. That means, in an hour Ryan will be 50 miles away from home. At that point, Jacob leaves home at a speed of 60 mph, so the gap between them closes by 10 miles each hour. That means that Jacob will take 5 hours to catch up, counting from when he left (how far is this workplace jeez?!?!?!?).
We could also represent this with a graph.
Hour 1: R = 50, J = 0 (Jacob leaves after this hour so it doesn't count for the answer)
Hour 2: R = 100, J = 60
Hour 3: R = 150, J = 120
Hour 4: R = 200, J = 180
Hour 5: R = 250, J = 240
Hour 6: R = 300, J = 300
find the missing side of the right triangle.
Answer:
Step-by-step explanation:
48
Answer:
51
Step-by-step explanation:
Pythagorean theorem
a^2+b^2=c^2
45^2+24^2
2025+576
2601=c^2
square root both sides
51=c
Hopes this helps please mark brainliest
5,10,20 Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form.
The given sequence is geometric sequence not arithmetic.
What is arithmetic sequence?An arithmetic sequence is a sequence in which the difference between every two consecutive terms is constant
What is the geometric sequence?A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value. It is found by taking any term in the sequence and dividing it by its preceding term.
Difference between arithmetic and geometric sequence:
An arithmetic sequence has a constant difference between each consecutive pair of terms
while
A geometric sequence has a constant ratio between each pair of consecutive terms.
Here, we have a sequence 5,10,20.
So a₁ = 5, a₂ = 10, a₃ = 20
Difference = a₃- a₂ = 20 - 0 = 10
a₂ - a₁ = 10 - 5 = 5
Since the difference is not constant, therefore the given sequence is not arithmetic.
Now ratio a₃/a₂ = 20/10 =2 and a₂/a₁ = 10/5 =2 which is same which shows the sequence is geometric.
Therefore, the sequence is geometric sequence.
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Solve the equation by factoring.
(x+2)(x + 7) = 0
A) (-2,-7)
C) (5,-8)
B) -5,5)
D) (6, 3)
Step-by-step explanation:
(x+2)(x+7) = 0
It is already factorised.
So, x = (-2,-7)
So, option A is correct
10 pionts!!!!
if f(x)=6x+5, find f(1)
Answer:
11
Step-by-step explanation:
Plug in 1 to the function:
f(x) = 6x + 5
f(1) = 6(1) + 5
f(1) = 6 + 5
f(1) = 11
Solve for x
-2x+6y=13
Jamar bought 22 chicken wings for $48.40. How much would it cost for 6 wings?
Answer: $13.2
Step-by-step explanation:
You can use proportions to find the cost(x):
[tex]\frac{22}{48.40} =\frac{6}{x} \\\\22x=6*48.4\\\\22x=290.4\\\\x=13.2[/tex]
Find the nth term of the sequence 90,81,72,63
Answer: 9.
Step-by-step explanation:
These are all multiples of 9, meaning that they can all be divided by 9 into a whole number.
90/9 =10
81/9 =9
72/9 =8
63/9 =7
Answer:
9:N
Step-by-step explanation:
90-9=81
81-9=72
72-9=63
The same number (9) is used to fing the sum of the next number in the sequence therefore that is your nth term
CAN SOMEONE DO THE ESSAY PART
The two triangles in the first figure is congruent by the ASA (angle-side-angle) axiom of congruency.
First diagram:
In ΔABC and ΔDEF we have :
∠C = ∠F
∠B = ∠E
BC = FE
∴ΔABC ≅ ΔDEF (by ASA axiom of congruency)
Second diagram:
In ΔABC and ΔDEF we have :
AB = XZ
BC = ZY
CA = XY
∴ΔABC ≅ ΔXYZ (by SSS axiom of congruency)
Third diagram:
In ΔKLM and TSU we have :
KL = TS
∠K = ∠U
∠M = ∠S
∴ΔKLM ≅ ΔTSU (by AAS axiom of congruency)
Fourth diagram:
In ΔABC and XYZ we have :
AB = YZ
BC = ZX
∠C = ∠Z
∴ΔABC ≅ ΔXYZ (by SAS axiom of congruency)
Fifth diagram:
No the two triangles are not congruent , they are similar.
AAA axiom is not for congruency, it is for similar triangles.
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Eric rode his small motor bike 5 4/5 miles in 1/3 of an hour what is his average speed per mile
The Average speed is 17.4 mph.
What is Average speed?The average speed is calculated by dividing the total distance travelled by the total amount of motion time.
The overall distance the object covers in a given amount of time is its average speed. A scalar value represents the average speed. It has no direction and is indicated by the magnitude.
Average speed = Distance travelled/ Time taken
Given:
Distance = 5 4/5 = 29/5 miles
Time= 1/3 hours
So, Average speed = Distance travelled/ Time taken
Average speed= 29/5 x 3/1
= 87/5
= 17.4 mph
Hence, the Average speed is 17.4 mph.
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HELP!! 25 POINTS
Simplify the expression to a + bi form:
√36+ √-75+ √1-√-108
Answer: 7-i√3
Step-by-step explanation:
√36+ √-75+ √1-√-108
6 + √75i + 1 - √108i
7 + 5i√3 - 6i√3
7-i√3