Answer:
a) [tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}}) [/tex]
And replacing we got:
[tex]\bar X \sim N(\mu=25, \frac{4}{\sqrt{30}}= 0.730) [/tex]
b) [tex] z =\frac{27-25}{\frac{4}{\sqrt{30}}}= 2.739[/tex]
And using the normal standard distribution table and the complement rule we got:
[tex] P(z>2.739) =1- P(z<2.739) = 1-0.997= 0.003[/tex]
Step-by-step explanation:
From the info given if we define the random variable X as "amount of saturated fat in a daily serving of a particular brand of breakfast cereal " we know that the distribution of X is given by:
[tex] X \sim N(\mu =25, \sigma =4)[/tex]
Part a
For this case the sample size would be n =30 and then the distribution for the sample mean would be given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}}) [/tex]
And replacing we got:
[tex]\bar X \sim N(\mu=25, \frac{4}{\sqrt{30}}= 0.730) [/tex]
Part b
We want to find this probability:
[tex] P(\bar X >27)[/tex]
And we can use the z score formula given by:
[tex] z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And replacing we got:
[tex] z =\frac{27-25}{\frac{4}{\sqrt{30}}}= 2.739[/tex]
And using the normal standard distribution table and the complement rule we got:
[tex] P(z>2.739) =1- P(z<2.739) = 1-0.997= 0.003[/tex]
Which choice is equal to the fraction below?
7/9
A. 0.777
O
B. 0.7
C. 0.77777777...
Answer:
0.77777777777...
Step-by-step explanation:
7/9 = 7 divided by 9
7 divided by 9 = 0.77777777777...
Where are the asymptotes for the following function located? f (x) = StartFraction 14 Over (x minus 5) (x + 1) EndFraction
Answer:
2 vertical asymptotes occurring at x = 5 and x = -1
Step-by-step explanation:
given
[tex]f(x) = \frac{14}{(x-5)(x+1)}[/tex]
recall that asymptotic occur at the locations that will make the equation undefined. In this case, the asymptote will occur at x-locations which will cause the denominator to become zero (and hence undefined)
Equating the denominator to zero,
(x-5)(x+1) = 0
(x-5) =0
x = 5 (first asymptote)
or (x+1) = 0
x = -1 (2nd asymptote)
We want to find the asymptotes of the given function.
There are two vertical asymptotes, one at x =5 and the other at x = -1.
First, we can briefly describe what an asymptote is.
An asymptote is a tendency to a given value that never reaches the actual value.
For example, we have vertical asymptotes (that tend to infinity or negative infinity) when we have a quotient with a denominator equal to zero.
Then, for our function:
[tex]f(x) = \frac{14}{(x-5)*(x +1)}[/tex]
We need to find the values of x such that the denominator becomes zero.
Is ratter easy to see that if x = 5, or x = -1, the denominator becomes equal to zero, then we will have two vertical asymptotes, one at x = 5 and other at x = -1.
If you want to learn more, you can read:
https://brainly.com/question/4084552
I need help to solve this grid question
Answer:
20 x 20 grid = 1066.67 cm wire
Step-by-step explanation:
Using unitary method
9 grid = 24 cm wire
1 grid = [tex]\frac{24}{9}[/tex] cm wire
Multiplying both sides by 400 (20 x 20)
400 grid = [tex]\frac{24}{9} * 400[/tex] cm
20 x 20 grid = 1066.67 cm wire
PLEASE HELP***
solve for x
Answer:
x =8
Step-by-step explanation:
The angles are vertical angles which means they are equal
4x+112 = 9x+72
Subtract 4x from each side
112 = 5x+72
Subtract 72 from each side
40 = 5x
Divide each side by 5
40/5 =x
8 =x
Answer: [tex]x=8[/tex]
Step-by-step explanation: Because they are opposite angles, they can be assumed to be equal to each other. Therefore, you can set the two equations equal to each other, creating [tex]9x+72=4x+112[/tex], and from there you can subtract [tex]4x[/tex] as well as [tex]72[/tex] from both sides to get [tex]5x=40[/tex]. Then, divide both sides by [tex]5[/tex] to get [tex]x=8[/tex].
On a coordinate plane, 2 triangles are shown. Triangle A B C has points (negative 4, 4), (negative 4, 1), and (0, 1). Triangle W R S has points (0, negative 1), (1.75, 1.5), (5, negative 1). In the diagram, △ABC ≅ △WRS. What is the perimeter of △WRS? 10 units 11 units 12 units 13 units
Answer:
(C)12 Units
Step-by-step explanation:
Triangle WRS has points W(0, -1), R(1.75, 1.5), and S(5, -1).
[tex]WR=\sqrt{(1.75-0)^2+(1.5-(-1))^2}=\dfrac{\sqrt{149}}{4}[/tex]
[tex]WS=\sqrt{(5-0)^2+(-1-(-1))^2}=\sqrt{25}=5[/tex]
[tex]RS=\sqrt{(5-1.75)^2+(-1-1.5)^2}=\dfrac{\sqrt{269}}{4}[/tex]
Perimeter of Triangle WRS
[tex]= \dfrac{\sqrt{149}}{4}+5+\dfrac{\sqrt{269}}{4}\\\approx 12$ Units[/tex]
Answer:
c
Step-by-step explanation:
took it on edge
What does mode mean
Answer:
MODE IS WHEN A NUMBER APPEARS MORE OFTEN IN A SET OF NUMBERS
Step-by-step explanation:
Example 2,3,8,6,5,3,4 , the mode is 3 because it appears more often
Have a great day
Can someone help me please
Answer:
35
Step-by-step explanation:
Angle 4 and angle 2 are alternate interior angles.
Alternate interior angles are equal.
Answer:
m∠2 = 35°
Step-by-step explanation:
∠4 is the corresponding angle to the angle right of ∠3. The angle right of ∠3 is vertical to ∠2, so they are both congruent. Therefore, m∠2 = 35°
You can also use the Alternate Interior Angles Theorem to state that ∠4 and ∠2 are congruent.
What are the solution(s) to the quadratic equation 50 - x² = 0?
O x = 425
0 x = +675
x = 5/2
no real solution
Answer:
The answer is C.
Step-by-step explanation:
[tex]50-x^2=0[/tex]
[tex]x^2=50[/tex]
[tex]x=\pm \sqrt{50} =\pm \sqrt{25*2}=\pm 5\sqrt{2}[/tex]
The answer is C (I am assuming that it isn't 5/2).
eBookThe manager of the Danvers-Hilton Resort Hotel stated that the mean guest bill for a weekend is or less. A member of the hotel's accounting staff noticed that the total charges for guest bills have been increasing in recent months. The accountant will use a sample of future weekend guest bills to test the manager's claim.a. Which form of the hypotheses should be used to test the manager's claim
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is
The manager of the Danvers-Hilton Resort Hotel stated that the mean guest bill for a weekend is $600 or less. A member of the hotel’s accounting staff noticed that the total charges for guest bills have been increasing in recent months. The accountant will use a sample of
weekend guest bills to test the manager’s claim.
a. Which form of the hypotheses should be used to test the manager’s claim? Explain.
1) H0:μ ≥ 600
Ha:μ < 600
2) H0:μ ≤ 600
Ha:μ > 600
3) H0:μ=600
Ha:μ≠600
b. What conclusion is appropriate when H0 cannot be rejected?
c. What conclusion is appropriate when H0 can be rejected?
Solution:
a) the hypotheses should be used to test the manager’s claim is
H0:μ ≤ 600
Ha:μ > 600
This is because the already known or assumed mean guest bill for a weekend is 600 or less. This forms the null hypothesis. The alternative is the opposite of the null hypothesis. Since the alternative states that it is increasing, the sign,> would be used.
b) If H0 cannot be rejected, it means that there is no sufficient evidence to reject H0 at the given level of significance.
c) if H0 can be rejected, it means that there is sufficient evidence to reject H0 at the given level of significance.
Please answer this correctly
Answer:
It’s a 1/2 chance it’s heads.
Step-by-step explanation:
Because there’s two sides
Answer:
1/2
Step-by-step explanation:
The probability of getting heads is 1 out of 2.
1/2
When you flip a coin, you either get heads or tails.
Make the appropriate conclusion. Choose the correct answer below. A. RejectReject H0. There is insufficientinsufficient evidence at the alphaαequals=0.100.10 level of significance to conclude that the true mean heart rate during laughter exceeds 7171 beats per minute. B. Do not rejectDo not reject H0. There is insufficientinsufficient evidence at the alphaαequals=0.100.10 level of significance to conclude that the true mean heart rate during laughter exceeds 7171 beats per minute. C. RejectReject H0. There is sufficientsufficient evidence at the alphaαequals=0.100.10 level of significance to conclude that the true mean heart rate during laughter exceeds 7171 beats per minute. D. Do not rejectDo not reject H0. There is sufficientsufficient evidence at the alphaαequals=0.100.10 level of significance to conclude that the true mean heart rate during laughter exceeds 7171 beats per minute.
Answer:
a) Option D is correct.
H0: μ = 71
Ha: μ > 71
b) Option F is correct
z > 1.28
c) z = 2.85
d) Option C is correct.
Reject H0.There is sufficient evidence at the α = 0.10 level of significance to conclude that the true mean heart rate during laughter exceeds 71 beats per minute.
Step-by-step explanation:
a) For hypothesis testing, the first thing to define is the null and alternative hypothesis.
The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.
While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.
This question aims to test the the true mean heart rate during laughter exceeds 71 beats per minute.
Hence, the null hypothesis is that there isn't sufficient evidence to say that the true mean heart rate during laughter exceeds 71 beats per minute. That is, the true mean doesn't exceed 71 beats per minute.
And the alternative hypothesis is that there is sufficient evidence to say that the true mean heart rate during laughter exceeds 71 beats per minute.
Mathematically,
The null hypothesis is represented as
H₀: μ = 71
The alternative hypothesis is represented as
Hₐ: μ > 71
b) Using z-distribution, the rejection area is obtained from the confidence level at which the test is going to be performed. Since the hypothesis test tests only in one direction,
Significance level = (100% - confidence level)/2
0.10 = 10% = (100% - confidence level)/2
20% = 100% - (confidence level)
Confidence level = 100% - 20% = 80%
Critical value for 80% confidence level = 1.28
And since we are testing if the true mean heart rate during laughter exceeds 71 beats per minute, the rejection area would be
z > 1.28
c) The test statistic is given as
z = (x - μ)/σₓ
x = sample mean = 73.4
μ = 71
σₓ = standard error = (σ/√n)
σ = 8
n = Sample size = 90
σₓ = (8/√90) = 0.8433
z = (73.4 - 71) ÷ 0.8433
z = 2.846 = 2.85
d) Since the z-test statistic obtained, 2.85, is firmly in the rejection area, z > 1.28, we reject the null hypothesis, accept the alternative hypothesis and say that there is sufficient evidence at the α = 0.10 level of significance to conclude that the true mean heart rate during laughter exceeds 71 beats per minute.
Hope this Helps!!!
helpppppp , quick answer with work pleaseeee
Answer:
Step-by-step explanation:
[tex]\sqrt{x-2}+8=x\\\\\sqrt{x-2}=x-8\\[/tex]
Square both sides,
[tex]x-2=(x-8)^{2}\\\\x-2=x^{2}-2*x*8+8^{2}\\\\x-2=x^{2}-16x+64\\\\x^{2}-16x+64=x-2\\\\x^{2}-16x+64-x+2=0\\\\x^{2}-17x+66=0[/tex]
Sum = - 17
Product = 66
Factors = -6 , -11
x² - 6x -11x + (-6)*(-11) = 0
x(x - 6) -11(x - 6) = 0
(x-6) (x - 11) = 0
x -6 = 0 ; x - 11 = 0
x = 6 ; x =11
Here, x = 6 is a extraneous solution
How do i solve this? Please help me find the answer.
Answer:
Step-by-step explanation:
The tangent lines meet the radii at 90 degrees.
The way the diagram is drawn, the following formula will work
<AOB + <OAC + OBC + 10 = 360
<OAC = 90
<OBC = 90
<AOB + 90 + 90 + 10 = 360
<AOB + 190 = 360
<AOB = 360 - 190
<AOB = 170
Which answer shows 2.13786 times 10 Superscript 4 written in standard form?
Answer:
Answer:
21378.6
Step-by-step explanation:
You move the decimal point four places towards the right.
Answer:
21378.6
Step-by-step explanation:
At the grocery store, Cory has narrowed down his selections to 6 vegetables, 6 fruits, 7 cheeses, and 5 whole grain breads. He wants to use the Express Lane, so he can only buy 15 items. In how many ways can he choose which 15 items to buy if he wants all 6 fruits?
Answer:
48620
Step-by-step explanation:
There are 6 fruits and 18 non-fruits. Cory wants to buy all 6 fruits, and 9 of the 18 non-fruits.
The number of ways he can choose 6 fruits from 6 is ₆C₆ = 1.
The number of ways he can choose 9 non-fruits from 18 is ₁₈C₆ = 48620.
The total number of combinations is 1 × 48620 = 48620.
Simply -5+2(x-3)+7x :)
Answer:
9x-11
Step-by-step explanation:
-5+2(x-3)+7x
Distribute
-5 +2x -6 +7x
-11 +9x
9x-11
Answer:
[tex]= 9x - 11 \\ [/tex]
Step-by-step explanation:
[tex] - 5 + 2(x - 3) + 7x \\ - 5 + 2x - 6 + 7x \\ - 5 - 6 + 2x + 7x \\ - 11 + 9x \\ = 9x - 11[/tex]
Divide up the number 480 in a ratio of 3:5.
Answer:
180:300
Step-by-step explanation:
You first divide 480 by 8 because 3+5= 8 and then you multiply that answer (60) by 3 to get 180 and then you multiply it by 5 to get 300. So you get the ratio of 180:300.
Which represents two rays that intersect at a common endpoint
An angle is the intersection of two noncollinear rays at a common endpoint. The rays are called sides and the common endpoint is called the vertex.
Suppose the Acme Drug Company develops a new drug, designed to prevent colds. The company states that the drug is equally effective for men and women. To test this claim, they choose a simple random sample of 100 women and 200 men from a population of 100,000 volunteers. At the end of the study, 38% of the women caught a cold; and 51% of the men caught a cold. Based on these findings, can we reject the company's claim that the drug is equally effective for men and women? Use a 0.05 level of significance.
a) Hypothesis: (In both symbols and words)
b) Decision rule:
c) Calculation:
d) Conclusion:
Answer:
a) Null hypothesis: the drug is equally effective for men and women (company's claim)
Alternative hypothesis: the drug effectiveness significantly differs for men and women.
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]
b) If the P-value is smaller than the significance level, the null hypothesis is rejected. If not, the null hypothesis failed to be rejected.
c) In the explanation.
d) As the P-value (0.0342) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the drug effectiveness significantly differs for men and women.
The company's claim is rejected.
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim of the company, will be stated in the null hypothesis. We will test if there is evidence against that claim to reject it or not.
Then, the test claim is that the drug effectiveness significantly differs for men and women.
The null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]
The significance level is 0.05.
The sample 1 (women), of size n1=100 has a proportion of p1=0.38.
The sample 2 (men), of size n2=200 has a proportion of p2=0.51.
The difference between proportions is (p1-p2)=-0.13.
[tex]p_d=p_1-p_2=0.38-0.51=-0.13[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{38+102}{100+200}=\dfrac{140}{300}=0.467[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.467*0.533}{100}+\dfrac{0.467*0.533}{200}}\\\\\\s_{p1-p2}=\sqrt{0.002489+0.001244}=\sqrt{0.003733}=0.061[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.13-0}{0.061}=\dfrac{-0.13}{0.061}=-2.1276[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):
[tex]P-value=2\cdot P(z<-2.1276)=0.0342[/tex]
As the P-value (0.0342) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the drug effectiveness significantly differs for men and women.
The least squares regression line minimizes the sum of the Group of answer choices differences between actual and predicted y values. absolute deviations between actual and predicted y values. absolute deviations between actual and predicted x values. squared differences between actual and predicted y values
Answer:
The least squares regression minimizes the sum of squared differences between actual and predicted y-values. This is the last option in your list of possible answers.
Step-by-step explanation:
Recall that when one performs the least square regression, one deals with what are called the "residuals". These are the differences in between the predicted "y-value" from the best fitting function, and the actual value of the dependent variable plotted (the actual y-value of the plotted points)
What the least square regression does is to find the best function parameters that minimize the sum of these squared residuals.
Solve the inequality and graph the solution set?
Answer:
0 < x < 8
Step-by-step explanation:
| x-4| < 4
There are two solutions one positive and one negative. Remember to flip the inequality on the negative solution
x-4 <4 and x-4 > -4
Add 4 to each side
x -4+4 <4+4 and x-4+4 > -4+4
x < 8 and x > 0
0 < x < 8
open circles at 0 and 8 and a line connecting them
A random sample of 1000 people was taken. Four hundred fifty of the people in the sample favored Candidate AT. The 95% confidence interval for the true proportion of people who favor Candidate A is a. .424 to .476. b. .419 to .481. c. .40 to .50. d. .45 to .55.
Answer:
[tex]0.45 - 1.96 \sqrt{\frac{0.45(1-0.45)}{1000}}=0.419[/tex]
[tex]0.45 + 1.96 \sqrt{\frac{0.45(1-0.45)}{1000}}=0.481[/tex]
And the 95% confidence interval would be given (0.419;0.481). And the best option would be:
b. .419 to .481
Step-by-step explanation:
We know the following info:
[tex]n = 1000[/tex] sample size selected
[tex]X= 450[/tex] represent the number of people who favored Candidate AT
The sample proportion would be:
[tex]\hat p=\frac{450}{1000}=0.45[/tex]
The confidence interval would be given by this formula
[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
For the 95% confidence interval the value of [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2=0.025[/tex], with that value we can find the quantile required for the interval in the normal standard distribution.
[tex]z_{\alpha/2}=1.96[/tex]
And replacing into the confidence interval formula we got:
[tex]0.45 - 1.96 \sqrt{\frac{0.45(1-0.45)}{1000}}=0.419[/tex]
[tex]0.45 + 1.96 \sqrt{\frac{0.45(1-0.45)}{1000}}=0.481[/tex]
And the 95% confidence interval would be given (0.419;0.481). And the best option would be:
b. .419 to .481
A child takes a bouquet of flowers and a group of small vases, and places a single flower in each vase, so
that no vases or flowers are left over. What mathematical relationship have they just established between
the bouquet of flowers and the group of vases?
Answer:
Step-by-step explanation:
this graph shows the outside temperature (in degrees celsius) over the course of 12 hours, starting at midnight (x=0)
Answer:
You can add graph by using the edit button and uploading a picture of the screen. if you then cut the picture before uploading so it just shows the graphand not the question. We cna then try answer for you.
Step-by-step explanation:
Generally graphs starting at point x=0 would show a different value for y by looking and counting up to its temperature.
if this shows positive it would be above the x axis line if it shows negative it would be a minus value below the x axis line under zero on y.
Therefore when we get to hr 2 and see this change you can count across and count up and see the rate of change is either 1,2,3,4,56,7,8 etc difference or 1x 2x 3x 4 x 5x 6 x as multiples.This then indicates a scale change at certain points.
Can someone explain to me? i don't understand it
Step-by-step explanation:
I will do 12 and 14 as examples.
12) Angles of a triangle add up to 180°.
m∠P + m∠Q + m∠R = 180
5x − 14 + x − 5 + 2x − 9 = 180
8x − 28 = 180
8x = 208
x = 26
m∠P = 5x − 14 = 116
m∠Q = x − 5 = 21
m∠R = 2x − 9 = 43
14) If two sides of a triangle are equal, then the angles opposite those sides are also equal.
(Conversely, if two angles are equal, then the sides opposite those angles are also equal. Such a triangle is called an isosceles triangle.)
BC ≅ BD, so m∠C = m∠D.
5x − 19 = 2x + 14
3x = 33
x = 11
m∠B = 13x − 35 = 108
m∠C = 5x − 19 = 36
m∠D = 2x + 14 = 36
Gravel is being dumped from a conveyor belt at a rate of 35 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 9 ft high? (Round your answer to two decimal places.)
Answer:
dh/dt ≈ 0.55 ft/min
Step-by-step explanation:
The volume is given by the formula ...
V = (1/3)πr²h
We have r = h/2, so the volume as a function of height is ...
V = (1/3)π(h/2)²h = (π/12)h³
Then the rates of change are related by ...
dV/dt = (π/4)h²·dh/dt
dh/dt = (4·dV/dt)/(πh²) = 4(35 ft³/min)/(π(9 ft)²)
dh/dt ≈ 0.55 ft/min
Please answer this correctly
Answer:
1/8 of the buckets
Step-by-step explanation:
There's one X for 1 1/2 cups which is greater than 1 1/4 cups but less than 1 3/4 cups. There are 8 pieces of data in total so our answer is 1/8 of the buckets.
Evaluate the expression 4/15÷x+0.4 for x if: x=1, x=4/9, x=1 1/3. Solve for each X. I need help Will give brainliest!
When x = 1, the expression evaluates to 2/3.
When x = 4/9, the expression evaluates to 1.
When x = 1 1/3, the expression evaluates to 3/5.
Let's evaluate the expression 4/15 ÷ x + 0.4 for each given value of x.
1) When x = 1:
4/15 ÷ 1 + 0.4 = 4/15 + 0.4 = 4/15 + 6/15 = 10/15 = 2/3
So, when x = 1, the expression evaluates to 2/3.
2) When x = 4/9:
4/15 ÷ (4/9) + 0.4 = 4/15 * (9/4) + 0.4 = 36/60 + 0.4 = 3/5 + 0.4 = 3/5 + 2/5 = 5/5 = 1
So, when x = 4/9, the expression evaluates to 1.
3) When x = 1 1/3 (or 4/3):
4/15 ÷ (4/3) + 0.4 = 4/15 * (3/4) + 0.4 = 12/60 + 0.4 = 1/5 + 0.4 = 1/5 + 2/5 = 3/5
So, when x = 1 1/3, the expression evaluates to 3/5.
Learn more about expression here
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You randomly select one card from a 52-card deck. Find the probability of selecting the four of spades or the ace of clubs.
(Type answer an integer or a fraction. Simplify your answer.)
Answer:
1/26
Step-by-step explanation:
There is 1 four of spades, and 1 ace of clubs.
So the probability is 2/52, or 1/26.
Answer:
P(four of spades or ace of clubs)= 1/26
Step-by-step explanation:
In a deck of 52 cards, there is one four of spaces and one ace of clubs. we want to find the probability of selecting those cards.
P(four of spades or ace of clubs)=four of spades+ace of clubs/total cards
There is 1 four of spades and 1 ace of clubs. 1+1=2
P(four of spades or ace of clubs)=2/total cards
There are 52 total cards in a deck.
P(four of spades or ace of clubs)=2/52
This fraction can be simplified. Both the numerator (top number) and denominator (bottom number) can be divided by 2.
P(four of spades or ace of clubs)= (2/2) / (52/2)
P(four of spades or ace of clubs)= 1/26
A pastry chef is making a batch of mini petit fours, which are little cakes, in the shape of cubes. To keep the nutritional value of each petit four consistent, the bakery manager wants each one to have a volume of 45cm3. What should the side length be, to the nearest hundredth, for each petit four? (Note: For volume of a cube, V=s3 where s=side length.)
Answer:
3.56 cm
Step-by-step explanation:
Cube is a 3D closed structure in which each adjacent side is perpendicular to each other and every side is equal to each other.
Let the side of cube be [tex]a[/tex] cm.
Please refer to attached image of cube for a clear look and feel of a cube with each side = a units.
Then, volume of cube is given by the formula:
[tex]V = a^3[/tex]
Here, we are given that:
[tex]V = 45\ cm^3[/tex]
[tex]\Rightarrow a^3 = 45\ cm^3\\\Rightarrow a =\sqrt[3] {45}\\\Rightarrow a ={45}^\frac{1}{3}\\\Rightarrow a = 3.56\ cm[/tex]
So, the answer is, Side of each petit four is, [tex]a = 3.56\ cm[/tex].