Answer:
Area = 0.019 m²
Step-by-step explanation:
stess = applied Force over Area
since stress = 0.987 MPa
and the force = 1.87 Kn
then Area = h * t
Q = F / (h * t)
0.987 mPa = 1.87 kN / (h* t)
since h * t = Area then 1.87 / 0.987
Area = 1.89 x 0.01 =
Area = 0.019 m²
A rectangular garden is 20 ft longer than it is wide. Its area is 3500 ft?. What are its dimensions?
Its width equals
Preview
and its length equals
Answer:
width of the garden is 50 ft and the length is 70 ft
Step-by-step explanation:
Solution:-
- We will denote the width and and the length of the rectangular garden as:
Width: x
Length: x + 20
- We are given the area ( A ) of the garden is 3500 ft^2. We are to determine for what dimensions is the area A = 3500 ft^2.
- Recall that the area ( A ) of a rectangle is the product of length and width as follows:
A = Length * width
A = x*( x + 20 )
3500 = x^2 + 20x
x^2 + 20x - 3500 = 0
- Use the quadratic formula to determine the value of ( x ):
[tex]x = \frac{-b +/- \sqrt{b^2 - 4ac} }{2a} \\\\x = \frac{-20 +/- \sqrt{20^2 - 4*-3500} }{2}\\\\x = \frac{-20 +/- 120 }{2} = -10 +/- 60\\\\x = -70 , 50[/tex]
- Ignore the negative value of ( - 70 ft ). Physical impractical to have a negative value. Hence, the width of the garden is 50 ft and the length is 70 ft
After collecting the data, Peter finds that the standardized test scores of the students in a school are normally distributed with mean 85 points and standard deviation 3 points. Use the Empirical Rule to find the probability that a randomly selected student's score is greater than 76 points. Provide the final answer as a percent rounded to two decimal places.
Answer:
Step-by-step explanation:
Given that:
the standardized test scores of the students in a school are normally distributed with:
mean = 85 points
standard deviation = 3 points
Using the empirical rule:
=85 - (3 × 3)
= 85 - 9
= 76
The given value of 76 points is 3 standard deviations below mean
Therefore;
the percent score between the given value of 76 points and the mean 85 points is:
99.7/2 = 49.85% ( since 99.7 data value lies within 3 standard deviation)
Also ; the percent of value above the mean score = 50%
Therefore, the probability that a student's score is greater than 76 points is
= (49.85 + 50 )%
= 99.85%
Answer:
mean=85
sd=3
85-3*3=76
its between 76 and 85=99.7/2=49.85%
50% mean above.
49.85+50=99.85%
Step-by-step explanation:
15. A manufacturer of electronic calculators is interested in estimating the fraction of defective units produced. A random sample of 800 calculators contains 10 defectives. a. Formulate and test the hypothesis to determine if the fraction defective exceeds 0.01. Use 0.05 significance level. b. Calculate a 95% CI for this problem. Does the CI agreed with your result on (a) explain.
Answer:
a
The Null hypothesis is [tex]H_o : p = 0.01[/tex]
The defect did not exceed 0.01
b
The 95% confidence interval is [tex]0.004801 < p < 0.020199[/tex]
Yes the CI agrees with the result in a because the value 0.01 fall within the CI
Step-by-step explanation:
From the question we are told that
The sample size is n = 800
The number of defective calculators is k = 10
The population is [tex]p = 0.01[/tex]
The Null hypothesis is [tex]H_o : p = 0.01[/tex]
The Alternative hypothesis is [tex]H_a : P> 0.01[/tex]
Generally the proportion of defective calculators is mathematically represented as
[tex]\r p = \frac{k}{n}[/tex]
substituting values
[tex]\r p = \frac{10}{800}[/tex]
[tex]\r p = 0.0125[/tex]
Next is to obtain the critical value of [tex]\alpha[/tex] from the z-table.The value is
[tex]Z_{\alpha } = 1.645[/tex]
Now the test statistics is mathematically evaluated as
[tex]t = \frac{\r p - p }{ \sqrt{ \frac{p (1- p )}{n} } }[/tex]
substituting values
[tex]t = \frac{ 0.0125 - 0.01 }{ \sqrt{ \frac{0.01 (1- 0.01 )}{800} } }[/tex]
[tex]t = 0.71067[/tex]
Now comparing the values of t to the value of [tex]Z_{\alpha }[/tex] we see that [tex]t < Z_{\alpha }[/tex] hence we fail to reject the null hypothesis
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p (1-\r p )}{n} }[/tex]
where [tex]Z_{\frac{\alpha }{2} }[/tex] is the critical value of [tex]\frac{\alpha }{2}[/tex] which is obtained from the z-table.The value is
[tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.05 }{2} } = 1.96[/tex]
The reason we are obtaining critical value of [tex]\frac{\alpha }{2}[/tex] instead of [tex]\alpha[/tex] is because [tex]\alpha[/tex]
represents the area under the normal curve where the confidence level interval ( [tex]1- \alpha[/tex] ) did not cover which include both the left and right tail while
[tex]\frac{\alpha }{2}[/tex] is just the area of one tail which what we required to calculate the margin of error .
NOTE: We can also obtain the value using critical value calculator (math dot armstrong dot edu)
So
[tex]E = 1.96 * \sqrt{\frac{ 0.0125 (1-0.0125 )}{800} }[/tex]
[tex]E = 0.007699[/tex]
The 95% confidence interval is mathematically represented as
[tex]\r p - E < p < \r p - E[/tex]
substituting values
[tex]0.0125 - 0.007699 < p < 0.0125 + 0.007699[/tex]
[tex]0.004801 < p < 0.020199[/tex]
Now given the p = 0.01 is within this interval then the CI agrees with answer gotten in a
50 POINTS!!!! I ALSO GIVE BRAINLIEST, BUT YOU HAVE TO ANSWER QUICK Choose the correct graph of the given system of equations. A pair of linear equations is shown: y = −x + 1 y = 2x + 4 Which of the following statements best explains the steps to solve the pair of equations graphically? On a graph, plot the line y = −x + 1, which has y-intercept = −1 and slope = 1, and y = 2x + 4, which has y-intercept = 2 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = 1, and y = 2x + 4, which has y-intercept = 1 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = −2 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.
Answer:
D. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.
Step-by-step explanation:
Correct answer is in bold. Incorrect answer have the mistakes put between stars *** ***.
50 POINTS!!!! I ALSO GIVE BRAINLIEST, BUT YOU HAVE TO ANSWER QUICK Choose the correct graph of the given system of equations. A pair of linear equations is shown: y = −x + 1 y = 2x + 4 Which of the following statements best explains the steps to solve the pair of equations graphically?
A. On a graph, plot the line y = −x + 1, which has y-intercept = ***−1*** and slope = 1, and y = 2x + 4, which has y-intercept = 2 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution.
B. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = ***1***, and y = 2x + 4, which has y-intercept = 1 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution.
C. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = ***−2*** and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.
D. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.
Find the probability of each of the following, if Z~N(μ = 0,σ = 1).
(please round any numerical answers to 4 decimal places)
a) P(Z > -1.13) =
b) P(Z < 0.18) =
c) P(Z > 8) =
d) P(| Z | < 0.5) =
Answer: a) 0.8708, b) 5714, c) 0.000, d) 0.3830
Step-by-step explanation:
(a)
To find P(Z>-1.13):
Since Z is negative, it lies on left hand side of mid value.
Table of Area Under the Standard Normal Curve gives area = 0.3708
So,
P(Z>-1.13) = 0.5 + 0.3708 = 0.8708
(b)
To find P(Z<0.18):
Since Z is positive, it lies on right hand side of mid value.
Table of Area Under the Standard Normal Curve gives area = 0.0714
So,
P(Z<0.18) = 0.5 + 0.0714 = 0.5714
(c)
To find P(Z>8):
Since Z is positive, it lies on right hand side of mid value.
Table of Area Under the Standard Normal Curve gives area = 0.5 nearly
So,
P(Z>8) = 0.5 - 0.5 nearly = 0.0000
(d)
To find P(| Z | < 0.5)
that is
To find P(-0.5 < Z < 0.5):
Case 1: For Z from - 0.5 to mid value:
Table of Area Under the Standard Normal Curve gives area = 0.1915
Case 2: For Z from mid value to 0.5:
Table of Area Under the Standard Normal Curve gives area = 0.1915
So,
P(| Z | < 0.5) = 2 * 0.1915 = 0.3830
The Probability can be determine using z-Table. The z- table use to determine the area under the standard normal curve for any value between the mean (zero) and any z-score.
(a) The value of [tex]P(z>-1.13)=0.8708[/tex].
(b) The value of [tex]P(Z < 0.18) = 0.5714[/tex].
(c) The value of [tex]P(Z > 8) = 0.0000[/tex].
(d) The value of [tex]P(| Z | < 0.5) =0.3830[/tex].
Given:
The given condition is [tex]Z\sim N(\mu= 0,\sigma = 1).[/tex]
(a)
Find the value for [tex]P(Z > -1.13)[/tex].
Here Z is less than 1 that means Z is negative. So it will lies it lies on left hand side of mid value.
Refer the table of Area Under the Standard Normal Curve.
[tex]\rm Area = 0.3708[/tex].
Now,
[tex]P(Z > -1.13)=0.5 + 0.3708 = 0.8708[/tex]
Thus, the value of [tex]P(z>-1.13)=0.8708[/tex].
(b)
Find the value for [tex]P(Z < 0.18)[/tex].
Here Z is positive. So it will lies it lies on right hand side of mid value.
Refer the table of Area Under the Standard Normal Curve.
[tex]\rm Area = 0.0714[/tex].
Now,
[tex]P(Z <0.18)=0.5 + 0.0714 = 0.5714[/tex]
Thus, the value of [tex]P(Z < 0.18) = 0.5714[/tex].
(c)
Find the value for [tex]P(Z >8)[/tex].
Here Z is positive. So it will lies it lies on right hand side of mid value.
Refer the table of Area Under the Standard Normal Curve.
[tex]\rm Area \approx 0.5[/tex].
Now,
[tex]P(Z >8)\approx0.5 - 0.5 = 0.0000[/tex]
Thus, the value of [tex]P(Z > 8) = 0.0000[/tex].
(d)
Find the value for [tex]P(|Z| <0.05)[/tex].
Here Z is mod of Z, it may be positive or negative. Consider the negative value of Z.
Refer the table of Area Under the Standard Normal Curve.
[tex]\rm Area =0.1915[/tex].
Consider the positive value of Z.
Refer the table of Area Under the Standard Normal Curve.
[tex]\rm Area =0.1915[/tex].
Now,
[tex]P(|Z| <0.5)=2\times 0.1915 = 0.3830[/tex]
Thus, the value of [tex]P(| Z | < 0.5) =0.3830[/tex].
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Given the sample mean = 23.375, sample standard deviation = 5.29, and N = 40 for the low income group, Test the claim that the mean nickel diameter drawn by children in the low income group is greater than 21.21 mm. Test at the 0.01 significance level.
a) Identify the correct alternative hypothesis:
A. p > 21.21
B. p < 21.21
C. p = 21.21
D. μ < 21.21
E. μ > 21.21
F. μ = 21.21
Give all answers correct to 3 decimal places
b) The test statistic value is:_______
c) Using the Traditional method, the critical value is:_______
Answer:
Step-by-step explanation:
a. To identify the alternative hypothesis, we have to examine the claim
The claim is that the mean nickel diameter drawn by children in the low income group is greater than 21.21 mm
Thus, alternative hypothesis is μ > 21.21
b. The test statistics is
z score = x - u /(sd/√n)
Where x (sample mean) is 23.375, u is pop. mean is 21.21, sd is 5.29 and n (sample size) is 40
z = 23.375 - 21.21 /(5.29/√40)
z = 2.165 / (5.29/6.3246)
z = 2.165/0.8364
z = 2.588
c. The critical value is
Alpha for this case study is 0.01. Then the critical probability is 1 - (alpha/2) =
1 - (0.01/2) = 1 - 0.005 = 0.995
To express the critical value as a z score, find the z score corresponding to the critical probability using the z table. Which is 0.8389.
Harry is trying to complete his hill walking scouts badge. He is using a map with a scale of 1 cm : 2 km. To earn the badge he needs to walk 14 km. What is the distance he needs to walk on the map?
Answer:
7 cm
Step-by-step explanation:
14 / 2 = 7 cm
7cm is the distance Harry needs to walk on the map?
What is Distance?Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are.
Given that,
Harry is trying to complete his hill walking scouts badge.
He is using a map with a scale of 1 cm : 2 km.
To earn the badge he needs to walk 14 km.
Let the distance he needs to walk on the map is x.
By given data we write an equation
1/2=x/14
Apply Cross Multiplication
14/2=x
7=x
Hence, 7cm is the distance he needs to walk on the map.
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How much would $200 invested at 7% interest compounded annually be
worth after 5 years? Round your answer to the nearest cent.
AD) -
A. $280.51
B. $214.40
C. $270.00
D. S283.87
Work Shown:
A = P*(1+r/n)^(n*t) .... compound interest formula
A = 200(1+0.07/1)^(1*5) .... plug in given info
A = 200*(1.07)^5
A = 200*1.4025517307
A = 280.51034614
A = 280.51
3.01)Which statement best describes the area of the triangle shown below?
9
It is one-half the area of a rectangle of length 4 units and width 2 units.
It is twice the area of a rectangle of length 4 units and width 2 units.
O It is one-half the area of a square of side length 4 units.
Ont is twice the area of a square of side length 4 units.
Answer:
C. It is one-half the area of a square of side length 4 units.
Step-by-step explanation:
Hey there!
Well if a square has side lengths of 4 units,
the area would be 16 because of l*w.
Now the formula for the area of a triangle is,
b*h/2
b = 4
h = 4
4*4=16
16 ÷ 2 = 8
So the area of a square is 16 units^2 whereas the area of a triangle with the same dimensions is 8 units^2,
meaning the area of a triangle is one-half the area of a square.
Hope this helps :)
Use the given conditions to write an equation for the line in point-slope form
Passing through (7,3) and (4,4)
OA
1
1.
y-3 = - =(x-
5(x-4) or y-4 = - 3(x - 7)
B.
1
1
y-3= - 3(x-7) or y- 4= - 3(x - 4)
O C. y - 3 = 7(x + 7) or y-4= 4(x-3).
OD
1
1
y + 3 = - 3(x+7) or y+4= - 3(x+4)
Answer:
(Y-3)= -1/3(x-7)
Or
(Y-4)= -1/3(x-4)
Steb by step explanation:
The condition for the line is (7,3) and (4,4).
Point slope form of equation is in this format below.
(Y-y1)= m(x-x1)
We have the given parameters in the above format except the m
M = gradient
Gradient= (y2-y1)/(x2-x1)
Gradient=(4-3)/(4-7)
Gradient= 1/-3
Gradient= -1/3
So
(Y-y1)= m(x-x1)
(Y-3)= -1/3(x-7)
Or
(Y-4)= -1/3(x-4)
The graph of a polynomial is shown below. At which value of x does this polynomial have an extreme?
Answer:
A. x = 4.
Step-by-step explanation:
An extreme is the highest or lowest value of the function. In this case, the extreme of the parabola is the lowest point, or the vertex.
We can see that point is at about A. x = 4.
Hope this helps!
HELP! EASY! WILL GIVE BRAINLIEST!
Answer:
c
Step-by-step explanation:
3 = 1/2x + 1/2x + 1/2x.
Answer:
x =2
Step-by-step explanation:
3 = 1/2x + 1/2x + 1/2x
Combine like terms
3 = 3/2 x
Multiply each side by 2/3 to isolate x
3 * 2/3 = 2/3 * 3/2 x
2 =x
if the focus of an ellipse are (-4,4) and (6,4), then the coordinates of the enter of the ellipsis are
Answer:
The center is (1,4)
Step-by-step explanation:
The coordinates of the center of an ellipse are the coordinates that are in the middle of the two focus.
Then if we have a focus on [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], we can say that the coordinates for x and y can be calculated as:
[tex]x=\frac{x_1+x_2}{2}\\ y=\frac{y_1+y_2}{2}[/tex]
So, replacing [tex](x_1,y_1)[/tex] by (-4,4) and [tex](x_2,y_2)[/tex] by (6,4), we get that the center is:
[tex]x=\frac{-4+6}{2}=1\\ y=\frac{4+4}{2}=4[/tex]
Fill in the blanks.
(x+_)^2=x^2+14x+_
Step-by-step explanation:
(ax + b)² = a²x² + 2abx + b²
In this case, a = 1, so:
14 = 2b
b = 7
(x + 7)² = x² + 14x + 49
Write these as normal numbers
Hi there!! (✿◕‿◕)
⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐
A.) 7.2 x 10^-5 = 0.000000072
B.) 6.3 x 10^-9 = 0.0000000063
C.) 4.54 x 10^-5 = 0.0000454
D.) 7.041 x 10^-10 = 0.0000000007041
Hope this helped!! ٩(◕‿◕｡)۶
The numbers can be written as;
A.) 7.2 x 10^{-5} = 0.000000072
B.) 6.3 x 10^{-9} = 0.0000000063
C.) 4.54 x 10^{-5} = 0.0000454
D.) 7.041 x 10^{-10} = 0.0000000007041
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We are given the parameters
We need to Write these as normal numbers
A.) 7.2 x 10^{-5} = 0.000000072
B.) 6.3 x 10^{-9} = 0.0000000063
C.) 4.54 x 10^{-5} = 0.0000454
D.) 7.041 x 10^{-10} = 0.0000000007041
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Perform the indicated operation. kyz * 1/kyz answer choices is 0 1 and k^2 y^2 z^2
Answer:
1
Step-by-step explanation:
[tex]\frac{kyz}{1}*\frac{1}{kyz} =\frac{kyz}{kyz}=1[/tex]
TRIANGLE ABC IS DILATED BY A SCALE FACTOR OF 0.5 WITH THE ORIGIN AS THE CENTER OF DILATION, RESULTING IN THE IMAGE TRIANGLE A'B'C. IF A=(2,2). IF A (2,2), B= (4,3) AND C=(6,3), WHAT IS THE LENGTH OF LINE B'C'?
Answer: The length of the line B'C" is 1 unit.
Step-by-step explanation:
Given: Triangle ABC is dilated by a scale factor of 0.5 with the origin as the center of dilation , resulting in the image Triangle A'B'C'.
If A (2,2), B= (4,3) and C=(6,3).
Distance between (a,b) and (c,d): [tex]D=\sqrt{(d-b)^2+(c-b)^2}[/tex]
Then, BC [tex]=\sqrt{(3-3)^2+(6-4)^2}[/tex]
[tex]\\\\=\sqrt{0+2^2}\\\\=\sqrt{4}\\\\=2\text{ units}[/tex]
Length of image = scale factor x length in original figure
B'C' = 0.5 × BC
= 0.5 × 2
= 1 unit
Hence, the length of the line B'C" is 1 unit.
Find the unknown side length x write your answer in simplest radical form
A.24
B.4squareroot37
C.2squareroot154
D.5squareroot117
Answer:
(B)[tex]4\sqrt{37}[/tex]
Step-by-step explanation:
First, we determine the height of the triangle which we label as y.
Using Pythagoras Theorem.
[tex]25^2=7^2+y^2\\y^2=25^2-7^2\\y^2=576\\y=\sqrt{576}\\y=24[/tex]
In the smaller right triangle with hypotenuse, x
Base = 7-3 =4 Units
Height, y= 24 Units
Therefore, applying Pythagoras Theorem.:
[tex]x^2=24^2+4^2\\x^2=592\\x=\sqrt{592}\\ x=4\sqrt{37}[/tex]
Please help. I’ll mark you as brainliest if correct!
Answer:
Quantity (lbs) of type 1 candy x = 8
Quantity (lbs) of type 2 candy y = 17,5
Step-by-step explanation:
Let´s call "x" quantity (in pounds) of candy type 1 in the mixture, and "y" quantity (in pounds ) of candy type 2, then according to the problem statement.
x + y = 25,5
2,20*x + 7,30*y = 5,70 * 25,5 ⇒ 2,20*x + 7,30*y = 145,35
Then we have a two equation system
x + y = 25,5 ⇒ y = 25,5 - x
2,20*x + 7,30*y = 145,35 ⇒ 2,20*x + 7,30* (25,5 - x ) = 145,35
2,20*x + 186,15 - 7,30*x = 145,35
5,1*x = 40,8
x = 40,8/5,1
x = 8 lbs
And y = 25,5 - 8
y = 17,5 lbs
6th grade math , help me please:)
Answer:
(a) $7/ticket
(b) 3 cats/dog
(c) 10 ft/sec
(d) 16 cups/gal
Step-by-step explanation:
(a) $35 for 5 tickets
$35/(5 tickets) = $7/ticket
(b) 21 cats and 7 dogs
21 cats/(7 dogs) = 3 cats/dog
(c) 40 ft in 4 seconds
40 ft/(4 sec) = 10 ft/sec
(d) 48 cups for 3 gallons
48 cups/(3 gal) = 16 cups/gal
Home health aide trades in old car a gas mileage of 18 1/4 miles per gallon.starting with a full tank of gas in her new car she travels 390 7/8 miles it takes 14 3/4 gallons to fuel the tank. How many miles further can she travel on a full tank of gas with the new car if the gas tank hold 30 gallons of gas
Answer:
The new car travels 247.5 miles more than the old one on 30 gallons of gas.
Step-by-step explanation:
The fuel consumption of the old car was:
[tex]car_{old} = 18 + \frac{1}{4} = \frac{73}{4} \text{ miles per gallon}[/tex]
The new one can travel a distance of 390 7/8 miles by using 14 3/4 gallons of fuel, therefore the consumption is:
[tex]car_{new} = \frac{390.875}{14.75} = 26.5 \text{ miles per gallon}[/tex]
If the tank holds 30 gallons, on the old car the distance would be:
[tex]distance_{old} = 18.25*30 = 547.5 \text{ miles}[/tex]
On the new one it will be:
[tex]distance_{new} = 26.5*30 = 795 \text{ miles}[/tex]
So the new car is able to travel 247.5 miles more than the old one on 30 gallons of gas.
You take one ball randomly from a bag with 10 yellow, 5 orange and 5 green balls. What is the probability that you take a yellow ball.
1
1/4
10/15
1/2
Answer:
1/2
Step-by-step explanation:
The probability of taking a yellow ball can be found by dividing the number of yellow balls over the total number of balls.
P(yellow ball)= yellow balls / total balls
There are 10 yellow balls. There are a total of 20 balls. There are 20 because there are 10 yellow, 5 orange, and 5 green. When 10, 5, and 5 are added, the result is 20.
yellow balls = 10
total balls= 20
P(yellow ball)= yellow balls / total balls
P(yellow ball)= 10/20
The fraction 10/20 can be simplified. Both the numerator( top number) and denominator (bottom number) can be evenly divided by 10.
P(yellow ball)= (10/10) / (20/10)
P(yellow ball)= 1/(20/10)
P(yellow ball)= 1/2
The probability of taking a yellow ball is 1/2.
Assume that females have pulse rates that are normally distributed with a mean of mu equals 75.0 beats per minute and a standard deviation of sigma equals 12.5 beats per minute. Complete parts (a) through (c) below. a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 78 beats per minute.
Answer:
0.40517 is the probability
Step-by-step explanation:
The first thing to do here is to calculate the corresponding z-score
Mathematically;
z-score = x-mean/SD
from the question,
x = 78, mean = 75 and SD = 12.5
Plugging these values in the z-score equation, we have;
z-score = (78-75)/12.5 = 3/12.5 = 0.24
So the probability we want to calculate is that;
P(z < 0.24)
we can get this by using the standard normal distribution table,
The value according to the table is;
0.40517
Which Graph represents the solution to the compound inequality 4x +8< -16 or 4x + 8 > 4
Answer:
option 3
Step-by-step explanation:
4x+8<-16
x<-6
4x+8_>-16
x_>-1
(it's more and equal .so the circle has to be shaded and move to the right of -1)
Answer:C
Step-by-step explanation:
Find x round to the nearest tenth
Answer:
83.0
Step-by-step explanation:
We have all three sides and the only thing we're missing is the X angle. And that's okay!
All you have to do is plug in the numbers into each variable. In this case if you are going to solve for X, you should use this equation.
[tex]x^2=y^2+z^2-2yzcosX[/tex]
x = 17ft
y = 8ft
x = 16fi
Then you can algebraically solve for cosX, and then use the inverse of cosx to get the angle.
Eight less than four times a number is less than 56. What are the possible values of that number?
Answer:
The numbers should be less than 16 . The numbers can be 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ............15
Step-by-step explanation:
Eight less than four times a number is less than 56 . The expression can be written below
let
the number = a
4a - 8 < 56
add 8 to both sides
4a - 8 + 8 < 56 + 8
4a < 64
divide both sides by 4
a < 64/4
a < 16
The numbers should be less than 16 . The numbers can be 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ............15
How many odd 2 digit positive odd integers geater than 50 are there?
Answer:
25
Step-by-step explanation:
Let's break this down step by step:
"2 digit positive odd integers greater than 50"
So we start at 50
Don't exceed 99 since 2-digit limit
Any 2-digit integer greater than 50 will be positive (So that's a redundant statement)
Well...we know that from 50-99, is 50 integers counting by ones.
We know that half will be even and half will be odd.
With this we can say 50/2 == 25
Hence, there are 25 2 digit positive odd integers greater than 50.
Cheers.
Which of the following answer choice is a possible solution to the inequality 4y>10?
A. 7
B. 1/4
C. 2
Please prove your answer.
Answer:
7 is the answer
Step-by-step explanation:
if we put 1/4 or 2 then the statement will wrong so 7 is the right answer
Answer:
A
Step-by-step explanation:
If 4A (7) is greater than 10, then 4x7=28. 28 is greater than 10.
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Hope this helps you...
may someone assist me ?
Answer:
x = 6
Step-by-step explanation:
I will use some symbols, please refer to the image I attach to understand my answer.
Since BC = 2 using Thales theorem we get that
3/x = 2/4 then 3/x = 1/2 and 6 = x