Answer:
88.93% probability that he let through more than 2 goals if the opposite team made 60 shots on goal.
Step-by-step explanation:
For each shot, there are only two possible outcomes. Either he lets it through, or he does not. Shots are independent. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The goalkeeper of the USA ice hockey National Team, Jonathan Quick, saved 91.6% of shots during his entire career in the NHL.
So he let in a goal in 100 - 91.6 = 8.4% of the shots, so [tex]p = 0.084[/tex]
60 shots:
This means that [tex]n = 60[/tex]
Estimate the probability that he let through more than 2 goals if the opposite team made 60 shots on goal.
Either he lets two or less goals, or he lets more than 2. The sum of the probabilities of these outcomes is 1. So
[tex]P(X \leq 2) + P(X > 2) = 1[/tex]
We want [tex]P(X > 2)[/tex].
Then
[tex]P(X > 2) = 1 - P(X \leq 2)[/tex]
In which
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{60,0}.(0.084)^{0}.(0.916)^{60} = 0.0052[/tex]
[tex]P(X = 1) = C_{60,1}.(0.084)^{1}.(0.916)^{59} = 0.0285[/tex]
[tex]P(X = 2) = C_{60,2}.(0.084)^{2}.(0.916)^{58} = 0.0770[/tex]
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0052 + 0.0285 + 0.0770 = 0.1107[/tex]
[tex]P(X > 2) = 1 - P(X \leq 2) = 1 - 0.1107 = 0.8893[/tex]
88.93% probability that he let through more than 2 goals if the opposite team made 60 shots on goal.
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
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
1 2 3 4 5 6 7 8 9 10 TIME REMAINING 01:28:16 Ramon is graphing the function f(x) = 3(4)x. He begins by plotting the initial value. Which graph represents his initial step? On a coordinate plane, the point (0, 3) is graphed. On a coordinate plane, the point (0, 4) is graphed. On a coordinate plane, the point (3, 0) is graphed. On a coordinate plane, the point (4, 0) is graphed.
Answer:
A
Step-by-step explanation:
ITS A
Answer:
On a coordinate plane, the point (0, 3) is graphed. Also known As A .
Step-by-step explanation:
The answer is A ,I just did the test and got it correct .
A cyclist rode 40 miles before having a flat tire and than walking 5 miles to a service station. The cycling rate was four times the walking rate. The time spent cycling and walking was 5 hours. Find the rate at which the cyclist was riding.
Answer:
Step-by-step explanation:
Let x represent the walking rate of the cyclist.
If the cycling rate was four times the walking rate, it means that the cycling rate is 4x mph.
Time = distance/speed
Time spent during cycling is
Time = 40/4x = 10/x
Time spent during walking is
5/x
Since the total time spent cycling and walking is 5 hours, it means that
10/x + 5/x = 5
Cross multiplying by x, it becomes
10 + 5 = 5x
5x = 15
x = 15/5
x = 3
The cycling speed is 4x = 4 × 3 = 12 mph
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).
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.
A certain insecticide kills 60% of all insects in laboratory experiments. A sample of 7 insects is exposed to the insecticide in a particular experiment. What is the probability that exactly 2 insects will survive? Round your answer to four decimal places.
Answer:
0.2613
Step-by-step explanation:
Use binomial probability.
P = nCr p^r q^(n-r)
where n is the number of trials,
r is the number of successes,
p is the probability of success,
and q is the probability of failure (1-p).
P = ₇C₂ (0.6)⁵ (0.4)²
P = 0.2613
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.
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.
Which one of the following statements is true? *
1 point
tan 45° = 1
cos 30° = 1/2
sin 45° = 1/3
sin 90° = 0
Answer:
tan 45° = 1 = true
cos 30° = 1/2 = false
sin 45° = 1/3 = false
sin 90° = 0 = false
Step-by-step explanation:
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.
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
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!!!
Please answer this correctly
Hey there! :)
Answer:
P(factor of 40) ≈ 66.7%
Step-by-step explanation:
Begin by finding factors of 40 on the die:
1, 2, 4, 5.
Find probability of a factor of 40:
[tex]\frac{factors}{total}[/tex]
There are 4 possible factors on a 6-sided die. Therefore:
[tex]\frac{4}{6} = \frac{2}{3}[/tex]
Convert to percentage:
2/3 × 100 ≈66.7%. This is the probability for a factor of 40.
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
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:
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...
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
En una fiesta hubo 25 ordenes mas de coca cola que de pepsi si hubo un total de 113 cuantas coca colas se vendieron 1) 57 2)19 3)44 4)69
Answer:
4) 69
Step-by-step explanation:
Nos dicen que en una fiesta hubo 25 ordenes mas de coca cola que de pepsi y que en total fueron 113 pedidos, por lo tanto:
Sea C pedidos de coca cola
Sea P pedidos de pepsi
C + P = 113
C = P + 25
Reemplazamos:
P + 25 + P = 113
2*P = 113 - 25
P = 88/2
P = 44
Ahora para saber el numero de pedidos de coca cola:
C = 44 + 25
C = 69
Lo que quiere decir que fueron 4) 69 pedidos la respuesta correcta.
Work out the surface area of this cylinder,
12 cm
25 cm
Answer:
surface area = 74π
Step-by-step explanation:
The surface are of a cylinder is the sum of the area of the 2 circular base and the curved surface area.
A cylinder has 2 circular base and the curved surface region. Mathematically,
surface area = area of 2 circles + curved surface area
area of 2 circles = πr² + πr² = 2πr²
curved surface area = 2πrh
surface area = 2πr² + 2πrh
surface area = 2πr(r + h)
where
r = radius
h = height
assuming the r = 12 cm and h = 25 cm
Therefore, replacing the value in the formula
surface area = 2πr(r + h)
surface area = 2π(12 + 25)
surface area = 2π(37)
surface area = 74π
a triangle can be formed with side lengths 4 in, 5 in, and 8 in.
Answer:
true
Step-by-step explanation:
4 + 5 > 8
Answer:
yes
Step-by-step explanation:
For the lengths given to form a triangle, then the sum of any 2 sides must be greater than the measure of the third side.
4 + 5 = 9 > 8
4 + 8 = 12 > 5
5 + 8 = 13 > 4
The inequality theorem is true thus the 3 lengths form a triangle.
please help with this two thank you
Answer:
Part 1
a) Greatest possible weight range of gorillas = 60 kg.
b) 20 gorillas weigh 80 kg or less.
c) Midpoint weight of the modal group = 105 kg.
d) The estimate of the mean gorilla weight = 99 kg.
Part 2
a) The greatest range of the lengths of snakes = 250 cm.
b) 40 snakes have lengths between 1.5 m and 2.5 m.
c) Midpoint length of the modal group = 175 cm.
d) The estimate of the mean gorilla length = 154 cm.
Step-by-step explanation:
Part 1 - The Gorilla part
a) Greatest possible weight range of gorillas = (Maximum weight of gorillas on the table) - (Minimum weight of gorillas on the table)
= 120 - 60 = 60 kg
b) How many gorillas weigh 80 kg or less
6 gorillas weigh between 60 < W ≤ 70
14 gorillas weigh between 70 < W ≤ 80
So, 6 + 14 = 20 gorillas weigh 80 kg or less.
c) Midpoint weight of the modal group
To find the modal class, we first use (n+1)/2 th
where N = number of variables = 160
Modal weight will be (160+1)/2 = 80.5 weight
The 80.5th weight is in the 100 to 110 class. This is how we know
6 + 14 + 22 + 34 = 76
Indicating that the 80.5th weight is in the next class (100 < W ≤ 110)
The midpoint weight of the modal class is then
(100+110)/2 = 105 kg
d) To calculate the mean weight, we use the midpoint theory where we replace all the groups with the midpoint weight of each weight class.
Midpoint weight is W, frequency is f
W | f
65 | 6
75 | 14
85 | 22
95 | 34
105 | 40
115 | 44
The mean is given as
Mean = (Σfx)/(Σf)
Σfx = (65×6) + (75×14) + (85×22) + (95×34) + (105×40) + (115×44) = 15800
Σf = 160
Mean = (15800/160) = 98.75 kg = 99 kg to the nearest whole number.
Part 2 - The Snake part
a) Greatest possible range of lengths of snakes = (Maximum length of snakes on the table) - (Minimum length of snakes on the table)
= 250 - 0 = 250 cm
b) How many snakes are between 1.5 m and 2.5 m in length?
1.5 m = 150 cm, 2.5 m = 250 cm
19 snakes have lengths between 150 < L ≤ 200
21 snakes have lengths between 200 < L ≤ 250
So, 19 + 21 = 40 snakes have lengths between 1.5 m and 2.5 m
c) Midpoint length of the modal group
To find the modal class, we first use (n+1)/2 th
where N = number of variables = 72
Modal length will be (72+1)/2 = 36.5th length
The 36.5th length is in the 150 to 200 class. This is how we know
4 + 11 + 17 = 32
Indicating that the 36.5th length is in the next class (150 < L ≤ 200)
The midpoint length of the modal class is then
(150+200)/2 = 175 cm
d) To calculate the mean length, we use the midpoint theory where we replace all the groups with the midpoint length of each length class.
Midpoint length is L, frequency is f
L | f
25 | 4
75 | 11
125 | 17
175 | 19
225 | 21
The mean is given as
Mean = (Σfx)/(Σf)
Σfx = (25×4) + (75×11) + (125×17) + (175×19) + (225×21) = 11100
Σf = 72
Mean = (11100/72) = 154.167 cm = 154 cm to the nearest whole number.
Hope this Helps!!!
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
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.
Two buses leave Boston at the same time traveling in opposite directions. One bus travels at 53mph and the other at 64mph. How soon will they be 936 miles apart?
Answer:
8 hours
Step-by-step explanation:
because each hour that goes by the buses go a distance of 117 miles apart from each other (53+64) you must divide the total distance by the 117 mph distance for a total of 8 hours (936 / 117 = 8)
Answer:
8 hours
Step-by-step explanation:
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
https://brainly.com/question/16922619
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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].
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.
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.
Help me with this problem pleaseeee
Answer:
Step-by-step explanation:
in a square pyramid the base area plus the area of the triangular faces is equal to the total area so we take (9*5) *1/2=22.5 then we multiply 22.5 *4= 90 so we take 90 + 5*5 = 115 so the total area is 115