Answer:
[tex]10\sqrt{14} + 8\sqrt{21} + 30 \sqrt{3} +36\sqrt{2}\\\\[/tex]
Step-by-step explanation:
[tex]( 2 \sqrt7 + 3 \sqrt6)(5\sqrt2 + 4\sqrt3)\\\\= 2\sqrt7(5\sqrt2 + 4\sqrt3) + 3\sqrt6 ( 5\sqrt2 + 4\sqrt3)\\\\=10\sqrt{7 \times 2} + 8\sqrt{7 \times 3} + 15\sqrt{6 \times 2} + 12\sqrt{ 6\times 3}\\\\=10\sqrt{14} + 8\sqrt{21} + 15 \sqrt{12} +12\sqrt{18}\\\\= 10\sqrt{14} + 8\sqrt{21} + 15 \sqrt{4 \times 3 } +12\sqrt{9 \times 2}\\\\= 10\sqrt{14} + 8\sqrt{21} + 15 \sqrt{2^2 \times 3} +12\sqrt{3^2 \times 2}\\\\= 10\sqrt{14} + 8\sqrt{21} + 30 \sqrt{3} +36\sqrt{2}\\\\[/tex]
In a particular year, the mean score on the ACT test was 22.5 and the standard deviation was 5.3. The mean score on the SAT mathematics test was 526 and the standard deviation was 101. The distributions of both scores were approximately bell-shaped. Round the answers to at least two decimal places.
Question is incomplete ; The questions solved were picked from similar questions but different parameters. However, the solution pattern are exactly the same.
Answer:
- 0.0943
- 0.386
30.185
Step-by-step explanation:
Given :
ACT:
Mean score, m = 22.5
Standard deviation, σ = 5.3
SAT :
Mean score, m = 526
Standard deviation, σ = 101
1.)
Zscore for ACT score of 22:
Since the distribution is normal ; we use the relation ;
Zscore = (score - mean) / standard deviation
Score = 22
Zscore = (22 - 22.5) / 5.3 = - 0.0943
B.)
Zscore for SAT of 487
Zscore = (score - mean) / standard deviation
Score = 487
Zscore = (487 - 526) / 101 = - 0.386
C.)
ACT score, for ACT Zscore of 1.45
Zscore = (score - mean) / standard deviation
ZScore = 1.45
1.45 = (score - 22.5) / 5.3
1.45 * 5.3 = (score - 22.5)
7.685 = score - 22.5
Score = 7.685 + 22.5
Score = 30.185
Please help Quick this is hard so you’ll get brainliest thank you so much
Answer:
number 1: no
number 2: no
number 3: no
what is the value of digit 6 in9.78265.
Answer: uhh I think 60?
Step-by-step explanation:
the answer is 6p because after any value place is zero hoped I helped
The owner of a golf course wants to determine if his golf course is more difficult than the one his friend owns. He has 8 golfers play a round of 18 holes on his golf course and records their scores. Later that week, he has the same 8 golfers play a round of golf on his friend's course and records their scores again. The average difference in the scores (treated as the scores on his course - the scores on his friend's course) is 9.582 and the standard deviation of the differences is 15.9274. Calculate a 90% confidence interval to estimate the average difference in scores between the two courses.1) (13.73,-0.65).2) (-10.359,-4.021).3) (-9.259,-5.121).4) (-13.745,-0.635).5) (13.745, -0.635).
Answer:
The 90% confidence interval to estimate the average difference in scores between the two courses is (-1.088, 20.252).
Step-by-step explanation:
We have the standard deviation for the differences, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 8 - 1 = 7
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 7 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.8946
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.8946\frac{15.9274}{\sqrt{8}} = 10.67[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 9.582 - 10.67 = -1.088
The upper end of the interval is the sample mean added to M. So it is 9.582 + 10.67 = 20.252
The 90% confidence interval to estimate the average difference in scores between the two courses is (-1.088, 20.252).
Will give brainliest answer
Answer: 2/5x to the second.
may I have the brainiest? pls
write the formula in finding the volume of the following 3D figures. write your answer inside the box.
rectangular prism
_____________
pyramid
_____________
sphere
_____________
cone
_____________
that's all, please someone help me to this question.
I'm gonna brainliest you!!!
Step-by-step explanation:
V=whl
lwh/3
4/3πr^3
πr^2h/3
Answer:
SHEEEEEEESH
Step-by-step explanation:
The width of a rectangle is 2 cm less than its length. The perimeter is 52 cm. The length is:
14 cm.
12 cm.
9 cm.
None of these choices are correct.
Answer: 14 cm
Step-by-step explanation:
Rectangle:
Length = xWidth = x - 2x + x + (x - 2) + (x - 2) = 52
2x + 2(x - 2) = 52
2x + 2x - 4 = 52
4x = 52 + 4
4x = 56
x = 14
A tree cast a shadow of 30m long and a 2m stick casts one that is 3m long. As show in the below diagram how tall is the tree?
Answer:
20 mStep-by-step explanation:
We have similar triangles here.
BC║DE, AB║AD and AC║AE ⇒ ΔADE ~ ΔABCThe ratio of corresponding sides of similar triangles is same:
BC/DE = AC/AEBC / 2 = 30/3BC / 2 = 10BC = 2*10BC = 20 mTake the similar triangles,
→ ∆ADE ≈ ∆ABC
Now we can find,
The height of the tree in meters,
→ BC/DE = AC/AE
In this equation BC is the height of tree,
→ BC/2 = 30/3
→ BC/2 = 10
→ BC = 10 × 2
→ BC = 20
Hence, the height of the tree is 20 m.
Amy worked 37.5 hours last week.
She is paid £11.50 per hour.
Her total deductions last week were £116.30.
What was Amy’s net pay last week?
£
the time it takes a runner to complete a race is inversely related to the speed of the runner if a runner can complete a race in 40 minutes while running at 8 mph how long will it take the runner to complete the race running at 9 mph t
Solve for x. The triangles are similar.
The list of ingredients for chocolate brownies given at right will make 16 brownies. Use the list to decide how much of each ingredient is needed to make 6 brownies.
Given: Given that for 16 brownies we need
Butter- [tex]\frac{2}{3}[/tex] cups
unsweetened chocolate-5 ounces
sugar-1-1/2 cup
vanilla-2 teaspoons
eggs-2
flour- 1 cup
To find: The amount of ingredients to make 6 brownies.
Solution: The amount we need to make 6 brownies is,
Butter
[tex](\frac{2}{3}.16)/6\\=0.25125 cups[/tex]
unsweetened chocolate
[tex]\frac{5.6}{16}\\=\frac{30}{16}[/tex]ounces
sugar-0.5625 cup
vanilla-[tex]\frac{12}{16}[/tex]teaspoons
eggs-[tex]\frac{12}{16}[/tex]
flour- [tex]\frac{6}{16}[/tex] cup
what are the two points in the image and what is the midpoint?
One can observe the midpoint is [tex](-3,1)[/tex].
But in order to verify the observation we must use formula to compute the midpoint of the segment formed by the endpoints.
The formula for such midpoint is [tex](\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex] where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are endpoints.
Our endpoints are [tex](-5,-3)[/tex] and [tex](-1,5)[/tex], so our midpoint is
[tex](\frac{-5-1}{2}, \frac{-3+5}{2})=\boxed{(-3,1)}[/tex].
Hope this helps.
posters n tees sold 486 items yesterday; one-third of these were t-shirts.how many t-shirts sold? how many posters?
Answer:
162 t-shirts, 324 posters
Step-by-step explanation:
Assuming they only sold t-shirts and posters, you can find the amount of t-shirts sold by dividing 486 by 3, or multiplying it by 1/3. This equals 162. This is because one third were t-shirts. To find the rest you just subtract 162 from the total of 486, or multiply 162 by 2. (since you already know the amount of 1/3, 2/3 is double that.)
What is the correct line graph for y=3x+5?
Answer:
The equation y=−3x+5 is in slope intercept form, and represents a straight line in which -3 is the slope, and 5 is the y -intercept.
PLEASE HELP!!! Which number is a solution of the inequality x less-than negative 4? Use the number line to help answer the question. A number line going from negative 9 to positive 1.
Answer:
is it going to be 10.5
Step-by-step explanation:
I do not have any explanation
Answer: 0 (zero)
Step-by-step explanation:
Start Learning & start growing! edge2023
*DROPS THE MIC*
if cosA=3√2/5,then show that cos2A=11/25
Answer:
Step-by-step explanation:
Cos 2A = 2Cos² A - 1
[tex]= 2*(\frac{3\sqrt{2}}{5})^{2}-1\\\\=2*(\frac{3^{2}*(\sqrt{2})^{2}}{5^{2}})-1\\\\=2*\frac{9*2}{25} - 1\\\\=\frac{36}{25}-1\\\\=\frac{36}{25}-\frac{25}{25}\\\\=\frac{11}{25}[/tex]
Simplify this plz thanks
Answer:
[tex]\frac{1}{g^{5nd+10v+20dv} }[/tex]
Step-by-step explanation:
Question 3
A 70kg patient has approximately 8 pints of blood. The patient donates 470mL of blood.
Approximately what fraction of his body's blood is this? (one pint = 568mL)
Step-by-step explanation:
Given that,
The mass of a patient = 70 kg
A 70kg patient has approximately 8 pints of blood.
The patient donates 470mL of blood.
We know that,
1 pint = 568 mL
8 pints = 4544 mL
Required fraction,
[tex]\dfrac{470}{4544}=0.1\\\\=\dfrac{1}{10}[/tex]
So, the required fraction is approximately [tex]\dfrac{1}{10}[/tex].
Geometry Oddsseseyware
Please help asap I needs someone to find the addition property added
A
Step-by-step explanation:
you can notice that at step 2 9 is added on both sides that is the addition property of equality
True or False? The total surface area of a cube can be calculated using its volume.
Answer: false
Step-by-step explanation:
Surface Area Formula Surface Area Meaning
SA=2B+Ph Find the area of each face. Add up all areas.
SA=B+12sP Find the area of each face. Add up all areas.
SA=2B+2πrh Find the area of the base, times 2, then add the areas to the areas of the rectangle, which is the circumference times the height.
A telephone exchange operator assumes that 9% of the phone calls are wrong numbers. If the operator is correct, what is the probability that the proportion of wrong numbers in a sample of 448 phone calls would differ from the population proportion by more than 3%
Answer:
0.0264 = 2.64% probability that the proportion of wrong numbers in a sample of 448 phone calls would differ from the population proportion by more than 3%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
A telephone exchange operator assumes that 9% of the phone calls are wrong numbers.
This means that [tex]p = 0.09[/tex]
Sample of 448
This means that [tex]n = 448[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.09[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.09*0.91}{448}} = 0.0135[/tex]
What is the probability that the proportion of wrong numbers in a sample of 448 phone calls would differ from the population proportion by more than 3%?
More than 9% + 3% = 12 or less than 9% - 3% = 6%. Since the normal distribution is symmetric, these probabilities are the same, so we find one of them and multiply by 2.
Probability it is less than 6%
P-value of Z when X = 0.06. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.06 - 0.09}{0.0135}[/tex]
[tex]Z = -2.22[/tex]
[tex]Z = -2.22[/tex] has a p-value of 0.0132
2*0.0132 = 0.0264
0.0264 = 2.64% probability that the proportion of wrong numbers in a sample of 448 phone calls would differ from the population proportion by more than 3%
data in the bar graph to solve the following problems. Choose the letter of the correl answer.
Distance from Churh (meters)
250
210
190
200
175
150
150
100
50
C. 25m
1. How much farther does Paolo walk thạnIgpher? Joshua
Topher
A. 20m
B. 15 m
C. 10m
D. 5m
2. How much farther does Joshua walk than Lucas?
A. 15m
B. 20m
D. 30m
3. How much farther does Topher than Lucas?
A. 50m
B. 40m
C. 30m
D. 20m
4. If you combine Paolo's and Lucas' distance from the church and compare it against the combined
distance walked by Joshua and Topher, which combined distance is farther
from the church?
A. Joshua and Topher
C. Joshua and Paolo
B. Paolo and Lucas
D. Topher and Lucas
5. Find the average distance of the houses of the 4 friends from the church?
A. 181
B. 191
C. 180
Answer:
The answer is below
Step-by-step explanation:
The bar chart to the question is attached below.
The distance traveled by Paolo = 210 m, The distance traveled by Lucas = 150 m, The distance traveled by Jashua = 175 m, The distance traveled by Topher = 190 m
1) The farther distance walk by Paolo = The distance traveled by Paolo - The distance traveled by Topher = 210 m - 190 m = 20 m
2) The farther distance walk by Jasha = The distance traveled by Jashua - The distance traveled by Lucas = 175 m - 150 m = 25 m
3) The farther distance walk by Topher = The distance traveled by Topher - The distance traveled by Lucas = 190 m - 150 m = 40 m
4) Combined distance of Paolo's and Lucas = 210 m + 150 m = 360 m
Combined distance of Jashua and Topher = 175 m + 190 m = 365 m
Therefore the Combined distance of Jashua and Topher is more
5) Average distance = (210 + 150 + 175 + 190)/4 = 181.25 m
Chloe has a small dog and a large dog. Each day, the small dog eats 3/4 cup of dog food, and the large dog 2 1/2 cups of dog food. In one week, how much more dog food does the large dog eat than the small dog ?
A. 1 3/4 cups
B. 8 3/4 cups
C. 12 1/4 cups
D. 22 3/4 cups
Answer:
A
Step-by-step explanation:
small dog eats 3/4 cup each day
large dog eats 1 cup each day
~after 1 week (x7)~
small dog = 5.25 cups
large dog = 7 cups
(7-5.25=1.75)
= therefore 1 and 3/4 cups
Slope intercept
6times+5y=15
Answer:
y= (-6/5)x+3
Step-by-step explanation:
6x+5y=15
Divide everything by 5
(6/5)x + y = 3
Move (6/5)x to the other side of the = sign by subtracting
y= (-6/5)x + 3
That's your answer!
Hope it helps!
Jen recently rode her bicycle to visit her friend who lives 6 miles away. On her way there, her average speed was & miles per hour faster than on her way home. If jen
spent a total of 2 hours bicycling find the two rates.
Answer:
(1) +t+=+1.2+ hrs
Step-by-step explanation:
Which of the following is the intersection of the line AD and line DE?
Answer:
Point D
Step-by-step explanation:
The intersection(s) of lines represents where they cross or intersect. We can see that lines AD and DE cross or intersect as Point D, hence the answer being Point D.
Answer: Point D
Step-by-step explanation: The intersection of two figures is the set of points that is contained in both figures. In the diagram shown, D is the intersection of lines AD and DE because D is the point contained by both line AD and DE.
Help differentiate this
Answer:
[tex]\displaystyle y' = 20x^3 + 6x^2 + 70x + 9[/tex]
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Terms/CoefficientsExpand by FOILFunctionsFunction NotationCalculus
Derivatives
Derivative Notation
Derivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = (x^3 + 7x - 1)(5x + 2)[/tex]
Step 2: Differentiate
Product Rule: [tex]\displaystyle y' = \frac{d}{dx}[(x^3 + 7x - 1)](5x + 2) + (x^3 + 7x - 1)\frac{d}{dx}[(5x + 2)][/tex]Basic Power Rule [Derivative Property - Addition/Subtraction]: [tex]\displaystyle y' = (3x^{3 - 1}+ 7x^{1 - 1} - 0)(5x + 2) + (x^3 + 7x - 1)(5x^{1 - 1} + 0)[/tex]Simplify: [tex]\displaystyle y' = (3x^2+ 7)(5x + 2) + 5(x^3 + 7x - 1)[/tex]Expand: [tex]\displaystyle y' = 15x^3 + 6x^2 + 35x + 14 + 5(x^3 + 7x - 1)[/tex][Distributive Property] Distribute 5: [tex]\displaystyle y' = 15x^3 + 6x^2 + 35x + 14 + 5x^3 + 35x - 5[/tex]Combine like terms: [tex]\displaystyle y' = 20x^3 + 6x^2 + 70x + 9[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
find out the Range coefficient of the range
marks number of students
20-29 8
30-39 12
40-49 20
50-59 7
60-69 3
Answer:
0.4494
Step-by-step explanation:
Given :
marks number of students
20-29 8
30-39 12
40-49 20
50-59 7
60-69 3
The range Coefficient is obtained thus :
Range Coefficient = (Xm - Xl) / (Xm + Xl)
Where ;
Xm = Mid value of highest class = (60+69)/2 = 64.5
Xl = Mid value of lowest class = (20+29)/2 = 24.5
Range Coefficient = (64.5 - 24.5) / (64.5 + 24.5)
Range Coefficient = 40 / 89 = 0.4494