Answer:
Step-by-step explanation:
The maximum possible distance between two posts for the fence will be given by HCF ( highest common factor ) of 24 and 64
24 = 8 x 3
64 = 8 x 8
highest common factor is 8 .
So distance between two poles ( maximum separation ) will be 8 m .
Ans : 8 m .
find the perimeter of the quadrant whose radius is 21cm
Answer:
75 cm
Step-by-step explanation:
∅=90° , r = 21 cm
Arc length= (2πr∅)/360
=(2π×21×90)/360
=33 cm
Perimeter= arc length + 2(radius)
=33+2(21)
=33 + 42
= 75 cm
Solve for x. 3x-91>-87 AND 17x-16>18
Answer & Step-by-step explanation:
For this problem, we have two inequalities to solve for x.
3x - 91 > -87
17x - 16 > 18
Now that we know what our inequalities are, we will solve them as if we are solving for the value of x.
3x - 91 > -87
Add 91 on both sides.
3x > 4
The solution for the first inequality is 3x > 4
Now let's do the second inequality.
17x - 16 > 18
Add 16 on both sides.
17x > 34
Divide by 17 on both sides.
x > 2
The soultion for the second inequality is x > 2
Answer:
The answer is x>2
Step-by-step explanation:
Can someone help me solve parts (a) and (c) please? Thank you!
a) 4x +6
Add up all the sides to calculate perimeter
Answer:
a) 6x + 6
b) 15 x 24
c) see explanation
Step-by-step explanation:
a) 2x + x + 3 + 2x + x + 3 = 6x + 6
b) 6x + 6 = 78
6x = 72
x = 12
2(12) = 24
(12) + 3 = 15
15 x 24
c) 2x(x + 3) = 2x² + 6x
2(12)² + 6(12) = 288 + 72 = 360
15 x 24 is also 360
Which of the following is true? Tangent is positive in Quadrant I. Sine is negative in Quadrant II. Cosine is positive in Quadrant III. Sine is positive in Quadrant IV.
Answer:
A
Step-by-step explanation:
I had this question and got it right the user above explains it in detail
To test the belief that sons are taller than their fathers, a student randomly selects 13 fathers who have adult male children. She records the height of both the father and son in inches and obtains the following data. Are sons taller than their fathers? Use the alphaequals0.10 level of significance. Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.
Height of Father Height of Son
72.4 77.5
70.6 74.1
73.1 75.6
69.9 71.7
69.4 70.5
69.4 69.9
68.1 68.2
68.9 68.2
70.5 69.3
69.4 67.7
69.5 67
67.2 63.7
70.4 65.5
Which conditions must be met by the sample for this test? Select all that apply.
A. The sample size is no more than 5% of the population size.
B. The differences are normally distributed or the sample size is large.
C. The sample size must be large.
D. The sampling method results in a dependent sample.
E. The sampling method results in an independent sample.
Write the hypotheses for the test. Upper
H 0 :
H 1 :
Calculate the test statistic. t 0=?
(Round to two decimal places as needed.)
Calculate the P-value. P-value=?
(Round to three decimal places as needed.) Should the null hypothesis be rejected?
▼ Do not reject or Reject Upper H 0 because the P-value is ▼ less than or greater than the level of significance. There ▼ is or is not sufficient evidence to conclude that sons ▼ are the same height or are shorter than or are taller than or are not the same height as their fathers at the 0.10 level of significance. Click to select your answer(s).
Answer:
1) B. The differences are normally distributed or the sample size is large
C. The sample size mus be large
E. The sampling method results in an independent sample
2) The null hypothesis H₀: [tex]\bar x_1[/tex] = [tex]\bar x_2[/tex]
The alternative hypothesis Hₐ: [tex]\bar x_1[/tex] < [tex]\bar x_2[/tex]
Test statistic, t = -0.00693
p- value = 0.498
Do not reject Upper H₀ because, the P-value is greater than the level of significance. There is sufficient evidence to conclude that sons are the same height as their fathers at 0.10 level of significance
Step-by-step explanation:
1) B. The differences are normally distributed or the sample size is large
C. The sample size mus be large
E. The sampling method results in an independent sample
2) The null hypothesis H₀: [tex]\bar x_1[/tex] = [tex]\bar x_2[/tex]
The alternative hypothesis Hₐ: [tex]\bar x_1[/tex] < [tex]\bar x_2[/tex]
The test statistic for t test is;
[tex]t=\dfrac{(\bar{x}_1-\bar{x}_2)}{\sqrt{\dfrac{s_{1}^{2} }{n_{1}}-\dfrac{s _{2}^{2}}{n_{2}}}}[/tex]
The mean
Height of Father, h₁, Height of Son h₂
72.4, 77.5
70.6, 74.1
73.1, 75.6
69.9, 71.7
69.4, 70.5
69.4, 69.9
68.1, 68.2
68.9, 68.2
70.5, 69.3
69.4, 67.7
69.5, 67
67.2, 63.7
70.4, 65.5
[tex]\bar x_1[/tex] = 69.6
s₁ = 1.58
[tex]\bar x_2[/tex] = 69.9
s₂ = 3.97
n₁ = 13
n₂ = 13
[tex]t=\dfrac{(69.908-69.915)}{\sqrt{\dfrac{3.97^{2}}{13}-\dfrac{1.58^{2} }{13}}}[/tex]
(We reversed the values in the square root of the denominator therefore, the sign reversal)
t = -0.00693
p- value = 0.498 by graphing calculator function
P-value > α Therefore, we do not reject the null hypothesis
Do not reject Upper H₀ because, the P-value is greater than the level of significance. There is sufficient evidence to conclude that sons are the same height as their fathers at 0.10 lvel of significance
Write the equation of the line which passes
through the points (4,2) and (-3, 1)
Answer:
y = 1/3x + 4/7
Step-by-step explanation:
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Slope-Intercept Formula: y = mx + b
Step 1: Find slope m
m = (1 - 2)/(-3 - 4)
m = -1/-7
m = 1/7
y = 1/7x + b
Step 2: Find y-intercept b
1 = 1/7(3) + b
1 = 3/7 + b
b = 4/7
Step 3: Write linear equation
y = 1/3x + 4/7
1-Determine a solução dos sistemas abaixo pelo método de adição: a) {x + y = 5 {2x- y=9 b) {3x - y = 10 {x + y =18 Prfvr gente
a)
X + Y = 5
2X - Y = 9
X + 2X + Y - Y = 5 + 9
3X = 14
X = 14/3Para Y, basta substituir o valor de X em qualquer uma das 2 equacoes - arbitrariamente. Escolhendo a primeira:
X+ Y = 5
14/3 + Y = 5
Y = 5 - 14/3
Y = 1/3.........................
b)
3X - Y = 10
X + Y = 18
3X + X - Y + Y = 10 + 18
4X = 28
X = 7Para Y, basta substituir o valor de X em qualquer uma das 2 equacoes - arbitrariamente. Escolhendo a segunda:
X + Y = 18
7 + Y = 18
Y = 18 - 7
Y = 11How can I divide decimals and fin the correct quotient and remainder.?
Answer:
Add a zero to the remainder and a decimal point in the quotient. Then we can continue to divide decimals. We divide 64 by 5 and obtain 12 as a quotient and 4 as a remainder. Since the remainder is not zero, we can continue to get a decimal answer by adding a decimal point in the quotient and a zero to the remainder
Step-by-step explanation:
If x3 + ax2 – bx + 10 is divisible by x2 – 3x + 2,
find the values of
1) a-b
2) 2a-b
If the measure of angle 4 is (11 x) degrees and angle 3 is (4 x) degrees, what is the measure of angle 3 in degrees?
Answer:
is it 2
Step-by-step explanation:
A
man paid 15600
for a new
car. He
was given a discount of
7%. Find the marked price
of the car
hope it helps.I was reading the same chapter
Georgina has $5.60 in quarters and dimes. If Georgina has 14 more dimes than quarters, how many quarters does she have?
[I don't want the answer i just want someone to show me how the problem is set up because its confusing me...Thanks]
Answer:
She has 12 quarters.
Step-by-step explanation:
You have two unknowns, the number of quarters and the number of dimes. You need one equation per unknown, so you need two equations. One equation deals with the number of coins. The other equation deals with the values of the coins.
The first step is to choose variables. We can go with x and y, but I prefer to choose q and d, so I remember more easily what they represent.
Let q = number of quarters.
Let d = number of dimes.
Let's deal with the numbers of coins first.
"Georgina has 14 more dimes than quarters"
She has q number of quarters, but the number of dimes is 14 more than the number of quarters. d is 14 more than q. Our first equation is
d = q + 14
Now we deal with the values of the coins.
We don't know yet the actual numbers of dimes and quarters, so we use d and q to represent those numbers.
One dime is worth $0.10; d number of dimes is worth 0.1d.
A quarter is worth $0.25; q number of quarters is worth 0.25q.
The total value of the dimes and quarters is the sum of the values of the two sets of coins:
0.1d + 0.25q
We are told "Georgina has $5.60 in quarters and dimes."
This gives us our second equation.
0.1d + 0.25q = 5.6
Now we have a set of two equations in two variables:
d = q + 14
0.1d + 0.25q = 5.6
There are several methods for solving a system of equations. Since the first equation is already solved for a variable, d, we can use the substitution method.
We rewrite the second equation, but we substitute q + 14 for d in the second equation.
Second equation:
0.1d + 0.25q = 5.6
Substitute q + 14 for d:
0.1(q + 14) + 0.25q = 5.6
Distribute on the left side:
0.1q + 1.4 + 0.25q = 5.6
Combine like terms on the left side:
0.35q + 1.4 = 5.6
Subtract 1.4 from both sides:
0.35q = 4.2
Divide both sides by 0.35:
q = 12
There are 12 quarters.
(You are asked only the number of quarters, so you can stop here. I will continue to find also the number of dimes for 2 reasons. 1) You see how it's done, so it will help with other problems. 2) By finding the numbers of dimes and quarters, then we can check if our solution is correct, which I will do below at the end.)
Now we use the first equation, d = q + 14. We substitute 12 for q and solve for d.
d = q + 14
d = 12 + 14
d = 26
There are 26 dimes.
Check:
We check the numbers of coins:
26 - 12 = 14 The number of dimes is indeed 14 more than the number of quarters.
We check the values of the coins:
0.1(26) + 0.25(12) = 2.6 + 3 = 5.6 The value of the coins is indeed $5.60.
Our answer is correct.
A researcher performs a hypothesis test to test the claim that for a particular manufacturer, the mean weight of cereal in its 18 ounce boxes is less than 18 ounces. He uses the following hypotheses: H 0: μ = 18 vs H A: μ < 18 and finds a P-value of 0.01. Draw a conclusion about the cereal box weight at a significance level of 0.05.
Answer:
We conclude that the mean weight of cereal in its 18-ounce boxes is less than 18 ounces.
Step-by-step explanation:
We are given that a researcher performs a hypothesis test to test the claim that for a particular manufacturer, the mean weight of cereal in its 18-ounce boxes is less than 18 ounces.
Let [tex]\mu[/tex] = mean weight of cereal in its 18-ounce boxes.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 18 {mean that the mean weight of cereal in its 18-ounce boxes is equal to 18 ounces}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 18 {mean that the mean weight of cereal in its 18-ounce boxes is less than 18 ounces}
Also, it is given that the P-value is 0.01 and the level of significance is 0.05.
The decision rule based on the P-value is given by;
If the P-value of our test statistics is less than the level of significance, then we have sufficient evidence to reject our null hypothesis as our test statistics will fall in the rejection region.If the P-value of our test statistics is more than the level of significance, then we have insufficient evidence to reject our null hypothesis as our test statistics will not fall in the rejection region.Here, clearly our P-value is less than the level of significance as 0.01 < 0.05, so we have sufficient evidence to reject our null hypothesis as our test statistics will fall in the rejection region.
Therefore, we conclude that the mean weight of cereal in its 18-ounce boxes is less than 18 ounces.
Help the question is there
Answer:
y = 7 when x = -5
Step-by-step explanation:
First go to x = -5
Then go up to where you meet the green line
The y value is 7
y = 7 when x = -5
the perimeter of square is 76 cm find are of square
Answer:
Given the information above, the area of the square is 361 cm²
Step-by-step explanation:
A square is a shape with four equal sides. So, in order to find the area of the square, we must find the length of each individual side. We can do this by dividing the perimeter by 4 because a square has 4 equal sides meaning they have the same lengths.
The perimeter of the square is 76. So, let's divide 76 by 4.
76 ÷ 4 = 19
So, the lengths of each sides in the square is 19cm.
In order to find the area, we must multiply the length and the width together. Since a square has equal sides, then we will multiply 19 by 19 to get the area.
19 × 19 = 361
So, the area of the square is 361 cm²
Answer:
361 cm^2
Step-by-step explanation:
The area of a square can be found by squaring the side length.
[tex]A=s^2[/tex]
A square has four equal sides. The perimeter is the sum of all four sides added together. Therefore, we can find one side length by dividing the perimeter by 4.
[tex]s=\frac{p}{4}[/tex]
The perimeter is 76 centimeters.
[tex]s=\frac{76 cm}{4}[/tex]
Divide 76 by 4.
[tex]s=19 cm[/tex]
The side length is 19 centimeters.
Now we know the side length and can plug it into the area formula.
[tex]A=s^2\\s=19cm[/tex]
[tex]A= (19 cm)^2[/tex]
Evaluate the exponent.
(19cm)^2= 19 cm* 19cm=361 cm^2
[tex]A= 361 cm^2[/tex]
The area of the square is 361 square centimeters.
If you make $3.80 an hour plus tips, what is your paycheck for the week if you worked 40 hours and made $250.00 dollars in tips?
Answer:
$402
Step-by-step explanation:
Hello!
If you made 3.80 an hour and worked 40 we can multiply these to find the total amount you earned.
3.80 * 40 = 152
You also made 250 in tips so we add that to the total
152+250 = 402
The answer is $402
Hope this helps!
Use the motion map to answer the question.
Which scenario could be represented by the motion
map?
O A car speeds up to merge onto the freeway and
then continues at a constant velocity
O A car speeds up to pass a truck, then slows down
to a constant velocity.
O A car slows to stop at a stop sign. Once traffic is
clear, the car speeds up.
O A car slows to makes a U-turn, then continues in
the opposite direction.
Answer:
A car slows to stop at a stop sign. Once traffic is clear, the car speeds up.
Step-by-step explanation:
Answer:
C.) A car slows to stop at a stop sign. Once traffic is clear, the car speeds up.
Step-by-step explanation:
Please answer quickly! A radio telescope has a parabolic surface, as shown below. A parabola opening up with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 1 meter and its width from left to right is 20 meters. If the telescope is 1 m deep and 20 m wide, how far is the focus from the vertex?
Answer:
Basing on the description, a parabola checking with vertex at origin, the formula with vertex at origin can be used, x^2 = 4py. p is the focus therefore with the dimensions given, we get yourself a 0.25 and this is the distance of the focus to the vertex.
I need help ASAP!!
Can someone explain this? And answer it? I am so confused!!
Answer:
Step-by-step explanation: hope this helps
is 5.676677666777 a rational number
Answer:Yes, because all integers have decimals. No, because integers do not have decimals. No, because integers cannot be negative. Jeremy says that 5.676677666777... is a rational number because it is a decimal that goes on forever with a pattern.
Step-by-step explanation:
Latanya buys 5 yard of blue fabric and 8 yards of green fabric. the blue fabric cost $2 dollars more than the green fabric.she pays a total of $ 62. what would be the combined cost of 1 yard of blue fabric and one yard of green fabric?
Answer: $10
Step-by-step explanation:
let x = the price of green fabric, then x+2 = blue fabric price
8x+5(x+2)=62
8x+5x+10=62
13x+10=62
13x=52
x=4
price of green fabric=$4
price of blue fabric=$6
4+6=$10
PLEASE HELP QUICK, WILL MARK BRAINLIEST!
Solve for x: −6 < x − 1 < 9
5 < x < 10
−5 < x < 10
−5 > x > 10
5 > x > −10
Answer:
−5 < x < 10
Step-by-step explanation:
−6 < x − 1 < 9
Add 1 to all sides
−6+1 < x − 1+1 < 9+1
−5 < x < 10
Answer:
B
Step-by-step explanation:
Add one to everything
-5 < x < 10
Best of Luck!
Pls help, I don’t know how to fo
frustum of a cone is: = pi * l(R + r)
(l) = slant height of the frustum.
from 2929.645714 - 506.1257143
= 2423.52
= 2423.5cm
Answer:
from 2929.645714 - 506.1257143
= 2423.52
= 2423.5cm
how many are 6 raised to 4 ???
Answer:
[tex]\large \boxed{1296}[/tex]
Step-by-step explanation:
6 raised to 4 indicates that the base 6 has an exponent or power of 4.
[tex]6^4[/tex]
6 is multiplied by itself 4 times.
[tex]6 \times 6 \times 6 \times 6[/tex]
[tex]=1296[/tex]
Which of the following is an irrational number?
5 / 4
√5 / 7
1/ 8
3 / 5
Answer: [tex]\sqrt{5} /7[/tex]
Step-by-step explanation:
5/4 is not an irrational number because it is already in a fraction the same as 1/8 and 3/5.
The square root of 5 is not rational because it cannot be converted to a fraction or in other words is not a perfect square.
Answer:√5 / 7
Step-by-step explanation:
1. 3x + 6y = 3 and 7x + 3y = 7
ons for bo
Answer:
(1,0)
Step-by-step explanation:
3x + 6y = 3
7x + 3y = 7
Multiply the second equation by -2
-2( 7x + 3y = 7)
-14x -6y = -14
Add this to the first equation to eliminate y
3x + 6y = 3
-14x -6y = -14
--------------------
-11 x = -11
Divide by -11
x = 1
Now find y
3x + 6y = 3
3 +6y = 3
Subtract 3 from each side
6y = 0
y =0
Answer:
x = 1
y = 0
Step-by-step explanation:
3x + 6y = 3
7x + 3y = 7
=> 3y = 7 - 7x
=> y = -7/3x + 7/3
3x + 6(-7/3x + 7/3) = 3
=> 3x - 14x + 14 = 3
=> -11x = -11
=> -x = -11/11
=> -x = -1
=> x = 1
So, 3(1) + 6y = 3
=> 3 + 6y = 3
=> 6y = 0
=> y = 0/6
=> y = 0
So, x = 1
y = 0
Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles.
A. 10.5 cm
B. 3.4 cm
C. 8.5 cm
D. 12 cm
Answer:
12 cm is the right answer pls mark me brainliest
The height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles is 12 cm.
What is Area of Triangle?The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.
What is Heron's formula?Heron's formula, formula credited to Heron of Alexandria (c. 62 ce) for finding the area of a triangle in terms of the lengths of its sides. In symbols, if a, b, and c are the lengths of the sides:
Area = √s(s - a)(s - b)(s - c) where s is half the perimeter, or (a + b + c)/2.
Given:
Three sides are: 15cm, 25 cm and 2 cm
Now, Using Heron's formula
semi-perimeter= (25+ 20 + 15)/2
s= 30 cm
Now,
Area of triangle
=√s(s-a)(s-b)(s-c)
=√30* 5 * 10* 15
=√5*2*3*5*2*5*3*5
=5*5*2*3
=150 cm²
Again, area of triangle= 1/2* b* h
150= 1/2* 25* x
12cm= x
Learn more about Area of Triangle here:
https://brainly.com/question/9817285
#SPJ2
If x^2 -8x=48 and x<0, what is the value of x+10?
Answer:
6
Step-by-step explanation:
To calculate x+10, we first need to find x. To do this, we can use the first equation.
We are given the equation:
[tex]x^2-8x=48[/tex]
To solve for x, turn one side of the equation into 0 and solve. Therefore:
[tex]x^2-8x=48\\x^2-8x-48=0\\(x-12)(x+4)=0\\x=-4, 12[/tex]
So, the possible values for x are -4 and 12.
However, we are also told that x<0. In other words, x must be negative. Thus, we can remove 12. That leaves us with: x=-4.
So:
[tex]x+10\\(-4)+10\\=6[/tex]
I am visiting my friend Janette in Bristol. My journey takes a total time of 1 hour 26 minutes. I travel by train for 34 minutes, then walk at a rate of 1/2 mile per 10 minutes. How many miles do I walk for?
Answer:
2.6 miles
Step-by-step explanation:
1 hour 26 minutes= 86 minutes
86-34=52 total walk time
52 minutes= 5*1/2 miles
=2.5 miles walked
and 2 minutes.
so we need to find 1/5 of 1/2
(1/2)/5=0.1 mile
2.5+0.1=2.6 miles
Of the 40 specimens of bacteria in a dish, 3 specimens have a certain trait. If 5 specimens are to be selected from the dish at random and without replacement, which of the following represents the probability that only 1 of the 5 specimens selected will have the trait?1) (5/1)/(40/3)
2) (5/1)/(40/5)
3) (40/3)/(40/5)
4) (3/1)(37/4)/(40/3)
5) (3/1)(37/4)/(40/5)
Answer:
[tex]\frac{(^3_1)*(^{37}_4)}{(^{40}_5)}[/tex]
Step-by-step explanation:
The total number of ways in which 5 specimens can be selected from the dish at random is given as C(40, 5).
Since only one of the five specimens would have the trait, the number of ways of selecting the one specimen out of the 3 specimens with the trait is C(3, 1).
3 specimens have the trait therefore 37 specimens (40 - 3) do not have the trait. The number of ways in which the remaining 4 specimens out of the 5 spemimens that do not have the trait is C(37, 4).
Therefore, the probability that only 1 of the 5 specimens selected will have the trait = [tex]\frac{C(3,1)*C(37,4)}{C(40,5)} =\frac{(^3_1)*(^{37}_4)}{(^{40}_5)}[/tex]
