Answer:
Option d: n = 36, p = 0.97, x = 36.
Step-by-step explanation:
We are given that a soup company puts 12 ounces of soup in each can. The company has determined that 97% of can have the correct amount.
We have to describe a binomial experiment that would determine the probability that a case of 36 cans has all cans that are properly filled.
Let X = Number of cans that are properly filled
The above situation can be represented through binomial distribution;
[tex]P(X = x) = \binom{n}{x} \times p^{x} \times (1-p)^{n-x} ; x = 0,1,2,........[/tex]
where, n = number of trials (samples) taken = 36 cans
x = number of success = all cans are properly filled = 36
p = probabilitiy of success which in our question is probability that
can have the correct amount, i.e. p = 97%
So, X ~ Binom (n = 36, p = 0.97)
Hence, from the options given the correct option which describes a binomial experiment that would determine the probability that a case of 36 cans has all cans that are properly filled is n = 36, p = 0.97, x = 36.
In the triangle below, what is the length of the hypotenuse?
A. \|3
B. 3\|3
C. 6
D. 3\|2
Answer:
C
Step-by-step explanation:
So you can use the 30, 60, 90 degree triangle ratio of x: 2x: x√3
The 3 is the x, and the hypotenuse is the 2x, so it's 6
Answer:
C. 6
Step-by-step explanation:
I just finished the test and I got 100 percent
A bottler of drinking water fills plastic bottles with a mean volume of 999 milliliters (ml) and standard deviation 7 ml. The fill
volumes are normally distributed. What is the probability that a bottle has a volume greater than 992 mL?
1.0000
0.8810
0.8413
0.9987
Answer:
0.8413
Step-by-step explanation:
Find the z score.
z = (x − μ) / σ
z = (992 − 999) / 7
z = -1
Use a chart or calculator to find the probability.
P(Z > -1)
= 1 − P(Z < -1)
= 1 − 0.1587
= 0.8413
The required probability that a bottle has a volume greater than 992 mL is 0.84134. Option C is correct
Given that,
A bottler of drinking water fills plastic bottles with a mean volume of 999 milliliters (ml) and a standard deviation of 7 ml. The fill volumes are normally distributed. What is the probability that a bottle has a volume greater than 992 mL, is to be determined
Probability can be defined as the ratio of favorable outcomes to the total number of events.
We use Z-statistic to find out the probability,
z = (x − μ) / σ
x = raw score = 992 mL
μ = population mean = 999 mL
σ = standard deviation
z = [992 − 999]/7
z = -1
P-value from Z-Table:
P(x<992) = 0.15866
P(x>992) = 1 - P(x<992) = 0.84134
Thus, the required probability that a bottle has a volume greater than 992 mL is 0.84134
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Shannon went to an auto repair shop and paid $339.50, which included parts that cost $112 and 3.5 hours of labor. Joni went to an auto repair shop and paid $455, which included parts that cost $310 and 2.5 hours of labor. Which correctly compares the cost of the labor? Shannon paid $7 more per hour for labor. Shannon paid $7 less per hour for labor. Joni paid $85 more per hour for labor. Joni paid $85 less per hour for labor.
for labor. Joni paid $85 less per hour for labor. explanation:
The correct comparison of the cost of labor between Shannon and Joni is that Shannon paid $7 more per hour for labor.
What is the cost?It refers to the total amount of the expenditure done on a product in manufacturing or procuring.
What is labor cost?It refers to the expenditure done on procuring labor for the work.
How to calculate per hour labor cost?In our situation Shannon paid total $339.50 in which the cost of the parts is $112 and 3.5 hours of labor. So,
labor cost Shannon Paid=339.50-112
=$227.50
labor cost per hour=227.50/3.5
=$6.5 per hour
Joni paid total $455 in which the cost of spare parts is $310 and rest is labor
labor cost paid by Joni=455-310
=$145
labor cost per hour=145/2.5
=$58 per hour
So by doing comparing we found that Shannon had paid $6 per hour extra for labor.
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Consider the density curve plotted below:
Find PX < 6.4):
Find P(X> 4.8):
Answer:
[tex] P(X<6.4)= \frac{6.4*0.2}{2}= 0.64[/tex]
[tex] P(X>4.8) =1-P(X<4.8)= 1- \frac{4.8*0.15}{2}= 1-0.36= 0.64[/tex]
Step-by-step explanation:
Part a
We want to find:
[tex] P(X<6.4)[/tex]
And we just need to find the area below the curve until x=6.4, since we have a triangle we can do this:
[tex] P(X<6.4)= \frac{6.4*0.2}{2}= 0.64[/tex]
Part b
For this case we want to find this probability:
[tex] P(X>4.8)[/tex]
And we can use the complement rule and we got:
[tex] P(X>4.8) =1-P(X<4.8)= 1- \frac{4.8*0.15}{2}= 1-0.36= 0.64[/tex]
Part A: Factor 3x2c2 + 5xc2 − 2c2. Show your work. (4 points) Part B: Factor x2 + 6x + 9. Show your work. (3 points) Part C: Factor x2 − 9. Show your work. (3 points) (10 points)
Answer:
[tex]\boxed{\mathrm{view \: explanation}}[/tex]
Step-by-step explanation:
A) 3x²c² + 5xc² - 2c²
Factor c² from all terms in the expression.
c²(3x² + 5x - 2)
Factor 3x² + 5x - 2
c²(3x-1)(x+2)
B) x² + 6x + 9
x² + 3x + 3x + 9
Factor common terms.
x(x+3)+3(x+3)
Take x+3 common.
(x+3)(x+3)
C) x² - 9
x² -3²
Apply formula : a² - b² = (a+b)(a-b)
(x+3)(x-3)
Answer:
A) [tex]c^2(3x-1)(x+2)[/tex]
B) [tex](x+3)(x+3)[/tex]
C) [tex](x+3)(x-3)[/tex]
Step-by-step explanation:
Part A:
[tex]3x^2c^2+5xc^2-2c^2[/tex]
Taking [tex]c^2[/tex] common
[tex]c^2(3x^2+5x-2)[/tex]
Using mid term break formula
[tex]c^2 (3x^2+6x-x-2)[/tex]
[tex]c^2[3x(x+2)-1(x+2)][/tex]
[tex]c^2(3x-1)(x+2)[/tex]
Part B:
[tex]x^2 + 6x + 9.[/tex]
[tex](x)^2+2(x)(3)+(3)^2[/tex]
[tex](x+3)^2[/tex]
[tex](x+3)(x+3)[/tex]
Part C:
[tex]x^2-9[/tex]
[tex](x)^2-(3)^2[/tex]
[tex](x+3)(x-3)[/tex]
Find three consecutive odd integers so that the sum of twice the first, the second
and three times the third is 152.
Answer: 23, 25, 27
Step-by-step explanation:
Let the 3 consecutive odd numbers be x, x+2 and x+4.
So
2x+(x+2)+3(x+4)=152
2x + x + 2 + 3x + 12 = 152
6x+14=152
6x = 152 - 14
x=138/6
x=23
So, the numbers are 23, 25 and 27.
Solve for x: 125^(3x+7)=25^(5x−11)
Answer:
x = 43
Step-by-step explanation:
125^(3x+7)=25^(5x−11)
Rewriting the bases as powers of 5
125 = 5^3 and 25 = 5^2
5^3 ^ (3x+7) = 5^2^(5x-11)
We know a^b^c = a^ (b*c)
5^(3 * (3x+7)) = 5^(2*(5x-11))
Distribute
5^(9x+21) = 5^(10x-22)
The bases are the same so the exponents are the same
9x+21 = 10x-22
Subtract 9x from each side
9x+21 -9x = 10x-9x-22
21 = x-22
Add 22 to each side
21+22 = x-22+22
43 = x
Which set of ordered pairs represents a function? {(0,1), (1,3), (1,5) (2,8)}, {(0,0), (1,2), (2,6), (2,8)}, {(0,0), (0,2), (2,0), (2,4)}, {(0,2), (1,4), (2,6), (3,6)}
Answer:
The last set.
Step-by-step explanation:
The first 3 sets contain 'one-to-many' relations , for example (1, 3) and (1, 5) in set 1 and (0, 0) and (0, 2) in set 3 , so they are not functions.
The last set does not have any of these and is a function.
A person stands 15 ft from an elephant. Determine how tall the elephant is in feet, the given diagram.
Answer:
The height of the elephant is [tex]\dfrac{15}{\sqrt3}\ ft[/tex].
Step-by-step explanation:
It is given that,
Distance between a person and an elephant is 15 ft
The angle of elevation of the elephant is 30 degrees.
We need to find the height of the elephant. For this let us consider that height is h. So,
[tex]\tan\theta=\dfrac{P}{B}\\\\\tan(30)=\dfrac{h}{15}\\\\h=15\times \tan(30)\\\\h=\dfrac{15}{\sqrt3}\ ft[/tex]
So, the height of the elephant is [tex]\dfrac{15}{\sqrt3}\ ft[/tex].
The amount of carbon-14 present in a paint after t years is given by y equals y Subscript o Baseline e Superscript negative 0.00012 t Baseline . The paint contains 27% of its carbon-14. How old are the paintings?
Answer:
The painting is [tex]t = 10911.1 \ years \ old[/tex]
Step-by-step explanation:
From the question we are told that
The amount of carbon present after t year is
[tex]y(t) = y_o * e ^{-0.00012t}[/tex] {Note ; This is the function }
Here [tex]y(t)[/tex] is the amount of carbon-14 after time t
[tex]y_o[/tex] the original amount of carbon-14
Now given that the paint as at now contain 27% of the original carbon-14
Then it mean that
[tex]y(t) = 0.27 y_o[/tex]
So the equation is represented as
[tex]0.27 y_o = y_o * e ^{-0.00012t}[/tex]
=> [tex]0.27 = * e ^{-0.00012t}[/tex]
=> [tex]ln(0.27) = -0.00012t[/tex]
=> [tex]- 1.30933 = -0.00012t[/tex]
=> [tex]t = \frac{-1.30933}{-0.00012}[/tex]
=> [tex]t = 10911.1 \ years[/tex]
Find the value of x in the isosceles triangle shown below.
Answer:
the answer is x = sqrt 48
Step-by-step explanation:
Subtract the rational expressions: (x/x+2)-(2/x)
The measure of minor arc JL is 60°. Circle M is shown. Line segments M J and M L are radii. Tangents J K and L K intersect at point K outside of the circle. Arc J L is 60 degrees. What is the measure of angle JKL? 110° 120° 130° 140°
Answer:
120
Step-by-step explanation:
Answer: 120
Hope that helped!(:
Pleased help with this
Answer:
A
Step-by-step explanation:
The height of an object dropped from the top of a 144-foot building is given by . How long will it take the object to hit the ground?
They left off the equation but we can know it's
y(t) = h₀ - g t² / 2
That's
y(t) = 144 - 16 t²
It hits the ground when
0 = 144 - 16 t²
16 t² = 144
t² = 144 / 16 = 9
t = 3 seconds
Answer: 3 seconds
Brainliest for whoever gets this correct! What is the sum of the rational expressions below?
Answer:
second option
Step-by-step explanation:
x / x - 1 + 3x / x + 2
= x(x + 2) / (x - 1)(x + 2) + 3x(x - 1) / (x - 1)(x + 2)
= (x² + 2x) / (x² + x - 2) + (3x² - 3x) / (x² + x - 2)
= (4x² - x) / (x² + x - 2)
Find the value of y........
Answer:
hope this is right y=74
Step-by-step explanation:
have not done this since two years ago so...
but anyway 148-180 = 32
32 is that angle
if this were a right triangle my answer would be different but 148/2 still completes this triangle and somewhat makes sense.
The correct answer is 90.
what are the coordinates of the vertex of the function f(x) = x2 -12x +5?
Answer:
[tex]\huge\boxed{(6;\ -31)}[/tex]
Step-by-step explanation:
METHOD 1:Let: [tex]f(x)=ax^2+bx+c[/tex].
The coordinates of the vertex:
[tex](h;\ k)\to h=\dfrac{-b}{2a};\ k=f(h)=\dfrac{-(b^2-4ac)}{4a}[/tex]
We have
[tex]f(x)=x^2-12x+5\to a=1;\ b=-12;\ c=5[/tex]
Substitute:
[tex]h=\dfrac{-(-12)}{2(1)}=\dfrac{12}{2}=6\\\\k=f(6)=6^2-12(6)+5=36-72+5=-31[/tex]
METHOD 2:The vertex form of an equation of a quadratic function:
[tex]f(x)=a(x-h)^2+k[/tex]
We have:
[tex]f(x)=x^2-12x+5\to a=1[/tex]
Complete to the square [tex](a\pm b)^2=a^2\pm2ab+b^2[/tex]
[tex]x^2-12x+5=x^2-\underbrace{2(x)(6)}_{12x}+5=\underbrace{x^2-2(x)(6)+6^2}_{a^2-2ab+b^2}-6^2+5\\\\=\underbrace{(x-6)^2}_{(a-b)^2}-36+5=(x-6)^2-31\\\\h=6;\ k=-31\to(6;\ -31)[/tex]
What the answer now fast
sine(X) = opposite side / hypotenuse
sine(X) = (2√11) / (4√11)
sine(X) = (2/4)
sine(X) = 0.5
X = arcsine(0.5)
X = 30°
Answer: m∠x = 30°
Step-by-step explanation:
In a right triangle, if the short side of the right angle is Half the length of the hypotenuse, the triangle has angles of 30°, 60° and 90°
∠x is the smallest one, so m∠x = 30°
It is possible to figure the sine and get the angle from that, but in this case it might not be necessary. ;-)
Use the cubic model y = 6x3 - 5x2 + 4x – 3 to estimate the value of y when x = 2.
a 25
(b 33
c 48
d 79
Done
Try Again
-
Answer:
The answer is B.
Step-by-step explanation:
You have to substitute x = 2, into the equation of y :
[tex]y = 6 {x}^{3} - 5 {x}^{2} + 4x - 3[/tex]
[tex]let \: x = 2[/tex]
[tex]y = 6 {( 2)}^{3} - 5 {(2)}^{2} + 4(2) - 3[/tex]
[tex]y = 48 - 20 + 8 - 3[/tex]
[tex]y = 33[/tex]
from the top of a building 10m high the angle of depression of a stone lying on the horizontal ground is 60° . calculate the distance of the stone from the foot of the building
Answer:
14.29cm
Step-by-step explanation:
Height of the building=10cm
Angle of depression=60°
We are therefore asked to find the distance from the stone to the
the foot of the building;Therefore we use Tan ratio which is opp/adj;
Let the distance from the stone to the foot of the building be x;
10/x=Tan60°
10/x=1.7/1
We then cross multiply to get 1.7x=10
x=10/1.7
=10*10/1.7*10
=100/17
=14.29cm.
Solve the matrix equation.
Answer:
answer there
Step-by-step explanation:
hope it. was. helpful
Assume that y varies directly with
x, then solve.
If y=2when x=, find y when x=1
y =
Lisa is 34 years old. Two years ago, she was twice as old as her brother. How old is her brother now?
Answer:
18
Step-by-step explanation:
Two years ago, Lisa was 34 - 2 = 32 years old. If she was twice as old as her brother, he was 32 / 2 = 16 years old at that time. His age now will be 16 + 2 = 18.
Find the volume o the sphere.
Answer:
The volume of sphere is 267.95 units³.
Step-by-step explanation:
Given that the formula of volume of sphere is V = 4/3×π×r³ where r represents radius. Then, you have to substitute the values into the formula :
[tex]v = \frac{4}{3} \times \pi \times {r}^{3} [/tex]
[tex]let \: r = 4[/tex]
[tex]v = \frac{4}{3} \times \pi \times {4}^{3} [/tex]
[tex]v = \frac{4}{3} \times \pi \times 64[/tex]
[tex]v = \frac{256}{3} \times 3.14[/tex]
[tex]v = 267.95 \: {units}^{ 3} [/tex]
Describe how to simplify the expression
3^-6
3^-4
Answer:
For 3^-6 = 1/3^6 = 726 and for 3^-4 = 1/3^4 = 81
Step-by-step explanation:
ARE THE NUMBERS SEPARATED OR THEY ARE TO BE JOIN TOGETHER,IF THERE ARE SEPARATED THE SOLUTION IS GOING TO BE...
3^-6
using law of indices x^-a = 1/x^a
So 3^-6 = 1/3^6
Now find the power of 3^6
which is the same as 3×3×3×3×3×3 = 729
therefore 1/3^6 = 729
For 3^-4
using the above method
3^-4 is same as 1/3^4
which is equal to
finding the nominator
3×3×3×3 = 81
so the answer is 81
Simplify the following algebraic expression.
square root of 392x^7
Answer:
[tex] \sqrt{392 {x}^{7} } [/tex]
Simplify
that's
[tex] \sqrt{392} \times \sqrt{ {x}^{7} } \\ \\ = \sqrt{196 \times 2} \: \times \sqrt{ {x}^{7} } \\ \\ = 14 \sqrt{2} \times \sqrt{ {x}^{7} } \\ \\ = 14 \sqrt{2x ^{7} } [/tex]
Hope this helps you
How do I tell if scatterplot is linear?
Part 1 You will need to measure five different people. Record your measurements on a piece of paper. Using a tape measure or ruler, measure the length (in inches) of a person’s left foot and then measure the length (in inches) of that same person’s forearm (between their wrist and elbow). Refer to the diagrams below. You will have two measurements for each person. (An easy way to measure the length of a foot is to have your subject stand on a piece of paper. Then, trace their foot and measure the outline once they move off the paper.) To measure the forearm, measure inside the arm, between the wrist and the elbow. Part 2 Organize your data and find the rate of change. Create a table of the measurements for your data. Label the forearm measurements as your input and the foot measurements as your output. Select two sets of points and find the rate of change for your data. Describe your results. If you had to express this relation as a verbal statement, how would you describe it? Part 3 Compare rates of change. The equation below can be used to find the length of a foot or forearm when you know one or the other. (length of the foot) = 0.860 • (length of the forearm) + 3.302 If you let y = length of the foot and x = length of the forearm, this equation can be simplified to y = 0.860x + 3.302. Using this equation, how long would the foot of a person be if his forearm was 17 inches long? What is the rate of change of the equation from Part A? Compare the equation from Part A to your data. Are they the same? Which has a greater rate of change? Why do you think the values are different? Is the relation in your data a function? Why or why not? Could the equation in Part A represent a function? Why or why not? Explain your answer. For this option you will submit the details from all three parts. Submit your measurements, the table, and description that you created in Parts 1 and 2. Submit your answers to the questions from Part 3. Measurement of forearm (x) 10in. , 15in , 10in, 11in. , 12in. Measurement of left foot (y) 9in. 11in. . 8in. 9 11/16in. 11 1/4in.
Answer:
to be honest I'm not sure how to do this question plz answer my question plz
Step-by-step explanation:
to be honest I'm not sure how to do this question plz answer my question plz I'm so much home workout
A study compared surgery and splinting for subjects suffering from carpal tunnel syndrome. It was found that among 73 patients treated with surgery,
there was a 92% success rate. Among 83 patients treated with splints, there was a 72% success rate. Calculations using those results showed that if
there really is no difference in success rates between surgery and splints, then there is about 1 chance in 1000 of getting success rates like the ones
obtained in this study. Which statement cannot be said?
The better treatment for carpal tunnel syndrome is surgery.
The result has practical significance.
The recommended treatment for carpal tunnel syndrome is splinting.
The result has statistical significance.
Answer:
the answer is c
Step-by-step explanation:
because if the surgery has a 92% success rate and the splints have a 72% success rate then surgery would be recommended because it has a higher success rate