Answer:
ΔV = 865.51 mm^3
Step-by-step explanation:
In order to calculate the difference in volume between both baseballs you use the following formula for the volume of a sphere:
[tex]V=\frac{4}{3}\pi r^3[/tex] (1)
where r is the radius of he sphere.
You calculate the volume of each sphere:
First baseball:
radius = 23.2mm/2 = 11.61mm
[tex]V_1=\frac{4}{3}\pi (11.61mm)^3=6555.18\ mm^3[/tex]
Second baseball:
radius = 24.2mm/2 = 12.1mm
[tex]V_2=\frac{4}{3}\pi (12.10)^3=7420.70\ mm^3[/tex]
Then, the difference in the volumen of both spheres is:
[tex]\Delta V=V_2-V_1=7420\ mm^3-6555.18\ mm^3=865.51\ mm^3[/tex]
Find the amount of money in savings account if $3200 was deposited for 3 years at 40% interest compounded annually. Find the interest
Step-by-step explanation:
Formula for compound interest is given by
[tex]A = P(1 + R) ^{n} [/tex]
Where
A is the amount at the end of the period
P is the principal
R is the rate
n is the period
The interest = A - P
From the question
P = $ 3200
n = 3 years
R = 40%
So we have
[tex]A = 3200 \times 2.744[/tex]
A = $ 8780.80
The amount is $ 8780.80The interest is
$ 8780.80 - $3200
= $ 5580.80Hope this helps you
please help ASAP!!!!!!!!!
Answer:
sec B = 17 / 15
Step-by-step explanation:
Sec theta = hyp / adj
sec B = 17 / 15
Answer:
17/15
Step-by-step explanation:
The secant of an angle is the ratio of the hypotenuse to the adjacent angle (it is also the reciprocal of cosine).
secθ=hypotenuse/adjacent
sec(∠B)= hypotenuse/adjacent
The hypotenuse in this triangle is 17, because it is opposite the right angle or the little square.
sec(∠B)=17/adjacent
The side adjacent, or next to angle B is 15.
sec(∠B)= 17/15
This fraction cannot be reduced further, therefore the secant of angle B is 17/15.
2 (3z-4) <16 Which one of the following values of z is a solution for the inequality
Answer:
z < 4
Step-by-step explanation:
2(3z-4) < 16
Divide by 2 on both sides
3z-4 < 8
Add 4 to both sides
3z < 12
Divide by 3 on both sides
z < 4
A private jet can fly 1,095 miles in 3 hours with a tailwind but only 987 miles in 3 hours into a headwind find the speed of the jet in still air
Answer:
The speed of the jet is 347 mph and the speed of the wind is 18 mph.
Step-by-step explanation:
We have the following:
x = the speed of the jet in still air.
y = the speed of the wind
we know that the speed is equal to:
v = d / t
therefore the distance would be:
d = v * t
if we replace with the information of the exercise we have:
3 * (x + y) = 1095
3 * (x - y) = 987
we must solve this system of equations, add both equations and we are left:
3 * x + 3 * y = 1095
3 * x - 3 * y = 987
3 * x + 3 * y + 3 * x - 3 * y = 1095 + 987
6 * x = 2082
x = 2082/6 = 347
now to calculate y, we replace:
3 * (347 + y) = 1095
1041 + 3 * y = 1095
3 * y = 1095 - 1041
y = 54/3 = 18
The speed of the jet is 347 mph and the speed of the wind is 18 mph.
4x-2(4x-2) simplify in the lowest form
Answer:
-4x + 4
Step-by-step explanation:
4x - 2( 4x - 2 )
→ Expand out 2 ( 4x - 2 )
2 ( 4x - 2 ) = 8x - 4
→ Substitute the expanded bracket back into the expression
4x - (8x - 4)
→ Collect the 'x' values
-4x + 4
A square mesaures 80 yd on a side. Bob and Rob begin running from the same corner. Bob runs along a side to an adjacent corner, and Rob runs along a diagonal to an opposite corner. They arrive at their respective corners at the same time. If Bob's speed was 8mi/h, what was Rob's speed? Express your answer as a decimal to the nearest tenth.
Answer:
c = 11.3 mi/h
Step-by-step explanation:
Since Square has all of the same sides, hence bobs speed will be the same for all of the sides.
All of the sides are equal in a square
=> Let's consider the two sides along with the diagonal a right angled triangle
=> [tex]c^2 = a^2 + b^2[/tex]
Where c is the speed of Rob along the diagonal and b and c is the speed of Bob along the side
=> [tex]c^2 = 8^2+8^2[/tex]
=> [tex]c^2 = 64+64[/tex]
=> [tex]c^2 = 128\\[/tex]
Taking sq root on both sides
=> c = 11.3 mi/h
F(x)=8*(1/2)^x table
Answer:
Show the table or make ur question a little more clear so I can help
Step-by-step explanation:
The marginal cost (dollars) of printing a poster when x posters have been printed is given by the following equation. C'(x)=x^-3/4 Find the cost of printing 142 more posters when 18 have already been printed.
The cost of printing 142 more posters when 18 have already been printed is $________.
(Round to the nearest cent as needed.)
Answer:
The cost of printing 142 more posters when 18 has already been printed is $5.57.
Step-by-step explanation:
We are given that the marginal cost (dollars) of printing a poster when x posters have been printed is given by the following equation C'(x)=x^-3/4.
The given equation is: [tex]C'(x) = x^{\frac{-3}{4} }[/tex]
The cost of printing 142 more posters when 18 have already been printed is given by;
Integrating both sides of the equation and using the limits we get;
[tex]\int_{a}^{b} C'(x) dx=\int_{18}^{142} x^{\frac{-3}{4}}dx[/tex]
As we know that [tex]\int\limits {x}^{n} \, dx = \frac{x^{n+1} }{n+1}[/tex] , so;
= [tex]\frac{x^{\frac{-3}{4}+1 } }{\frac{-3}{4}+1 } ]^{142} __1_8[/tex]
= [tex]\frac{x^{\frac{1}{4} } }{\frac{1}{4} } ]^{142} __1_8[/tex]
= [tex]4[x^{\frac{1}{4} } } ]^{142} __1_8[/tex]
= [tex]4[(142)^{\frac{1}{4} }- (18)^{\frac{1}{4} }} ][/tex]
= $5.57
Hence, the cost of printing 142 more posters when 18 has already been printed is $5.57.
Scores made on a certain aptitude test by nursing students are approximately normally distributed with a mean of 500 and a variance of 10,000. If a person is about to take the test what is the probability that he or she will make a score of 650 or more?
Answer:
0.0668 or 6.68%
Step-by-step explanation:
Variance (V) = 10,000
Standard deviation (σ) = √V= 100
Mean score (μ) = 500
The z-score for any test score X is:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
For X = 650:
[tex]z=\frac{650-500}{100}\\z=1.5[/tex]
A z-score of 1.5 is equivalent to the 93.32nd percentile of a normal distribution. Therefore, the probability that he or she will make a score of 650 or more is:
[tex]P(X\geq 650)=1-P(X\leq 650)\\P(X\geq 650)=1-0.9332\\P(X\geq 650)=0.0668=6.68\%[/tex]
The probability is 0.0668 or 6.68%
The probability that he or she will make a score of 650 or more is 0.0668.
Let X = Scores made on a certain aptitude test by nursing students
X follows normal distribution with mean = 500 and variance of 10,000.
So, standard deviation = [tex]\sqrt{10000}=100[/tex].
z score of 650 is = [tex]\frac{\left(650-500\right)}{100}=1.5[/tex].
The probability that he or she will make a score of 650 or more is:
[tex]P(X\geq 650)\\=P(z\geq 1.5)\\=1-P(z<1.5)\\=1-0.9332\\=0.0668[/tex]
Learn more: https://brainly.com/question/14109853
Students in management science class have just received their grades on the first test. The instructor has provided information about the first test grades in some previous classes as well as the final average for the same students. Some of these grades have been sampled and are as follow:
1st test Grade 98 77 88 80 96 61 64 95 79
Final average 93 78 84 75 84 64 66 95 86
Develop a regression model that could be used to predict the final average in the course based on the first test grade.
Predict the final average of a students who made an 83 on the first test.
Give the value of r and r2 for this model.
Interpret the value of r2 in the context of this problem.
Answer:
The regression model is:
y = 20.29 + 0.73·x
Step-by-step explanation:
In this case a regression model is to be formed to predict the final average in the course based on the first test grade.
Use Excel to form the regression model.
The output is attached below.
The regression model is:
y = 20.29 + 0.73·x
Predict the final average of a students who made an 83 on the first test as follows:
y = 20.29 + 0.73·x
= 20.29 + 0.73 × 83
= 80.88
The final average of a students who made an 83 on the first test would be 80.88.
From the output:
R² = 0.839
Then the correlation coefficient will be:
[tex]r=\sqrt{R^{2}}=\sqrt{0.839}=0.91597\approx 0.92[/tex]
The value of r is 0.92.
The coefficient of determination R² specifies the percentage of the variance in the dependent-variable (Y) that is forecasted or explained by linear regression and the forecaster variable (X, also recognized as the independent-variable).
In this case, the R² value of 0.839 implies that 83.9% of the variation in the final average can be explained by the grades in the first test.
Which is the simplified form of the expression 3(7/5x + 4) - 2(3/2 - 5/4x)?
1) -39/5x - 11/2
2)67/10x + 9
3) 3/10x + 5/2
4) 15 + 76/10x
Answer:
(67/10)x + 9 (answer [2])
Step-by-step explanation:
3(7/5x + 4) - 2(3/2 - 5/4x). after the indicated multiplication has been carried out, is:
(21/5)x + 12 - 3 + (5/2)x
Combining like terms, we get (4.2 + 2.5)x + 9, or
6.7x + 9, or (67/10)x + 9 (answer [2])
7x-x combine the like terms to create an equivelent expression
Answer:
6x
Step-by-step explanation:
7x - x
Factor out x
x( 7-1)
6x
Answer:
6x
Step-by-step explanation:
7x - x
Apply rule : a = 1a
x = 1x
7x - 1x
Factor out x.
(7 - 1)x
(6)x
Share £1200 in the ratio 3:5.
so you have the amount.
amount: 1200
then you have the ratio
ratio: 3:5
you have the count.
count: 2
and then you have the shares
shares: 8
and the amount per share is 150.00
so the total amount of shares is the sum of each person's ratio so,
so 1:5:2:3:9 = 1 + 5 + 2 + 3 +9 = 20 shares. hope that helps you..
What is the exact volume of the cylinder? Enter your answer, in terms of π, in the box. m³ $\text{Basic}$ $x$$y$$x^2$$\sqrt{ }$$\frac{x}{ }$ $x\frac{ }{ }$ $x^{ }$$x_{ }$$\degree$$\left(\right)$$\abs{ }$$\pi$$\infty$ A cylinder that is 2.5 m tall with a radius of 1.5 m
Answer:
[tex]5.625\pi[/tex] m³.
Step-by-step explanation:
The volume of a cylinder is found by calculating pi * r^2 * h.
In this case, h = 2.5, and r = 1.5.
pi * 1.5^2 * 2.5
= pi * 2.25 * 2.5
= pi * 5.625
So, the exact volume of the cylinder is [tex]5.625\pi[/tex] m³.
Hope this helps!
Answer: Volume of Cylinder: [tex]\pi r^{2} *h[/tex]
5.625π m.
Step-by-step explanation:
[tex]\pi r^{2} *h[/tex] Cylinder Area Formula
[tex]\pi *1.5^{2} *2.5[/tex] Substitution
[tex]\pi * 2.25 *2.5[/tex] Exponent
[tex]\pi *5.625[/tex] Multiply
[tex]5.625\pi[/tex] Answer
Letters a, b, c, and d are angles measures. Lines m and n are cut by transversal p. At the intersection of lines p and m, labeled clockwise, from uppercase left, the angles are: a, b, c, blank. At the intersection of lines p and n, labeled clockwise, from uppercase left, the angles are: blank, blank, d, blank. Which equation is enough information to prove that lines m and n are parallel lines cut by transversal p? Select three options. a = c a = d c = d b + c = 180° b + d = 180°
Answer:
b, c, e
Step-by-step explanation:
the reasons have to include an angle from both of the parallel lines. by using process of elimination it is b, c, e. I also got it right
Answer:
B. a=d
C. c=d
E. b + d=180°
Step-by-step explanation:
Got Correct On MyPath.
Determine whether the following statement is true or false. If it is false, rewrite it as a true statement. A double-blind experiment is used to increase the placebo effect. Choose the correct answer below. A. The statement is false. Double blinding has no effect on the placebo effect. B. The statement is false. Double blinding is used to increase the randomization. C. The statement is true. D. The statement is false. Double blinding is used to decrease the placebo effect.
Answer:
D. The statement is false. Double blinding is used to decrease the placebo effect.
Step-by-step explanation:
In a double blind study, neither researchers nor the participants know which group is receiving the placebo. If the researchers do not know which group took the medication, they cannot influence the behavior of this group, knowingly or nor, by suggesting how they should behave.
Therefore, a double-blind experiment is used to decrease the placebo effect.
I need help with this problem.
________________________Alike______________________
→ Both of the lines are proportional meaning they go through the origin.
→ Both of the lines have a positive slope meaning the slope goes towards the top right corner.
__________________________________________________
_____________________Difference_____________________
→ The 2 lines have different slopes, the first one has a slope of 1/3x whereas the 2nd one has a slope of 3x.
→ The points that create the lines are totally different, no two points are the same.
__________________________________________________
A restaurant operator in Accra has found out that during the partial lockdown, if she sells a plate of her food for GH¢20 each, she can sell 300 plates, but for each GH¢5 she raises the price, 10 less plates are sold.
Draw a table of cost relating to number of plates using 6 values of cost and its corresponding number of plates bought.
What price in GH¢ should she sell the plates to maximize her revenue?
Answer:
Step-by-step explanation:
First, note this parameters from the question.
We let x = number of $5 increases and number of 10 decreases in plates sold.
Our Revenue equation is:
R(x) = (300-10x)(10+5x)
We expand the above equation into a quadratic equation by multiplying each bracket:
R(x) = 3000 + 1500x - 3000x - 1500x^2
R(x) = -1500x^2 - 1500x + 3000 (collect like terms)
Next we simplify, by dividing through by -1500
= 1500x^2/1500 - 1500x/1500 + 3000/1500
= X^2 - x + 2
X^2 - x + 2 = 0
Next, we find the axis of symmetry using the formula x = -b/(2*a) where b = 1, a = 1
X = - (-1)/2*1
X = 1/2
Number of $5 increases = $5x1/2 = $2.5
=$2.5 + $20 = $22.5 ticket price gives max revenue.
Evaluate the expression when a=4 and y=-6.
-a+3y
a.
hi
Answer:
- 22Step-by-step explanation:
Given,
a = 4
y = -6
Now,
[tex] - a + 3y[/tex]
Plug the values
[tex] = - 4 + 3 \times ( - 6)[/tex]
Multiply the numbers
[tex] = - 4 + ( - 18)[/tex]
When there is a (+) in front of an expression in parentheses, the expression remains the same.
[tex] = - 4 - 18[/tex]
Calculate
[tex] = - 22[/tex]
Hope this helps..
Best regards!!
Answer:
14
Step-by-step explanation:
-4 + 3(6)
-4+18
14
Use the Quadratic Formula to solve the equation ? x^2-2x=-9
Answer:
x=(2+ √-32)/2 or x=(2- √-32)/2
Step-by-step explanation:
x^2 - 2x = -9
x^2 - 2x + 9 =0
x = 2± (√(-2)^2 - 4*1*9)/2*1
Use the quadratic formula in the expression using a=1, b= -2, c=9
x = 2±√4-36 /2
x = 2+√4-36 or x = 2 - √4 - 32 /2
x = (2+√-32) /2 or x=( 2 - √-32 )/2
The solution for the given quadratic equation are (2+i5.7)/2 or (2-i5.7)/2.
The given quadratic equation is x²-2x=-9.
What is the quadratic formula?Quadratic formula is the simplest way to find the roots of a quadratic equation.
The roots of a quadratic equation ax² + bx + c = 0 are given by x = [-b ± √(b² - 4ac)]/2a.
By comparing x²-2x+9=0 with ax² + bx + c = 0, we get a=1, b=-2 and c=9
Substitute a=1, b=-2 and c=9 in the quadratic formula, we get
x = [2±√(-2)²-4×1×9)]/2×1
= [2±√4-36]/2
= (2±i5.7)/2
x = (2+i5.7)/2 or (2-i5.7)/2
Therefore, the solution for the given quadratic equation are (2+i5.7)/2 or (2-i5.7)/2.
To learn more about the quadratic formula visit:
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The five numbers summary for a data set is shown below. What is the range of the data set? 3, 7, 11, 14, 16
Answer:
13
Step-by-step explanation:
The range of a set of data is the difference between the highest and lowest values in the set.
So, in order to find the range, you first order the data from least to greatest. Which it is already.
3, 7, 11, 14, 16
Then subtract the smallest value from the largest value in the set.
16 - 3 = 13
Hope this helps you out! : )
x² + 2x-3
f(x) =
x2 + 5x + 6
(a) What is the domain of the function? (Write your answer in interval notation.)
(b) Determine the equation of the vertical asymptotes of f. If there are none, write, 'None!
(C) Determine the equation of the horizontal asymptote of f. If there is none, write, 'None'.
(d) Find the y-intercept(s).
(e) Find the x-intercept(s).
Click to select your answer(s).
Answer:
x4+7x+3
Step-by-step explanation:
In the following problem, the expression is the right side of the formula for cos (alpha - beta) with particular values for alpha and beta. cos (79 degree) cos (19 degree) + sin (79 degree) sin (19 degree)
Identify alpha and beta in each expression.
The value for alpha: degree
The value for beta: degree
Write the expression as the cosine of an angle. cos degree
Find the exact value of the expression. (Type an exact answer, using fraction, radicals and a rationalized denominator.)
Answer:
1. [tex]\alpha = 79[/tex] and [tex]\beta = 19[/tex]
2. [tex]cos(60)[/tex]
3. [tex]cos(60) = \frac{1}{2}[/tex]
Step-by-step explanation:
Given
[tex]cos(\alpha - \beta )[/tex]
[tex]cos(79)cos(19) + sin(79)sin(19)[/tex]
Solving for [tex]\alpha[/tex] and [tex]\beta[/tex]
In trigonometry;
[tex]cos(\alpha - \beta ) = cos\alpha\ cos\beta + sin\alpha\ sin\beta[/tex]
Equate the above expression to [tex]cos(79)cos(19) + sin(79)sin(19)[/tex]
[tex]cos(\alpha - \beta ) = cos\alpha\ cos\beta + sin\alpha\ sin\beta[/tex] and [tex]cos(\alpha - \beta ) = cos(79)cos(19) + sin(79)sin(19)[/tex]
By comparison
[tex]cos\alpha\ cos\beta + sin\alpha\ sin\beta = cos(79)cos(19) + sin(79)sin(19)[/tex]
Compare expression on the right hand side to the left hand side
[tex]cos\alpha\ cos\beta = cos(79)cos(19) \\\\ sin\alpha\ sin\beta = sin(79)sin(19)[/tex]
This implies that
[tex]cos\alpha\ = cos(79)\\cos\beta = cos(19) \\\\ and\\\\sin\alpha\ = sin(79)\\sin\beta = sin(19)[/tex]
By further comparison
[tex]\alpha = 79[/tex] and [tex]\beta = 19[/tex]
Substitute [tex]\alpha = 79[/tex] and [tex]\beta = 19[/tex] in [tex]cos(\alpha - \beta )[/tex]
[tex]cos(\alpha - \beta ) = cos(79 - 19)[/tex]
[tex]cos(\alpha - \beta ) = cos(60)[/tex]
Hence, the expression is [tex]cos(60)[/tex]
Solving for the exact values;
Express [tex]cos(60)[/tex] as a difference of angles
[tex]cos(60) = cos(90 - 30)[/tex]
Recall that [tex]cos(\alpha - \beta ) = cos\alpha\ cos\beta + sin\alpha\ sin\beta[/tex]
So;
[tex]cos(90- 30 ) = cos(90) cos(30) + sin(90) sin(30)[/tex]
------------------------------------------------------------------------------------
In trigonometry;
[tex]cos(90) = 0[/tex]; [tex]cos(30) = \frac{\sqrt{3}}{{2}}[/tex]; [tex]sin(90) = 1[/tex]; [tex]sin(30) = \frac{1}{2}[/tex];
---------------------------------------------------------------------------
[tex]cos(90- 30 ) = cos(90) cos(30) + sin(90) sin(30)[/tex] becomes
[tex]cos(90- 30 ) = 0 * \frac{\sqrt{3}}{2} + 1 * \frac{1}{2}[/tex]
[tex]cos(90- 30 ) = 0 + \frac{1}{2}[/tex]
[tex]cos(90- 30 ) = \frac{1}{2}[/tex]
Hence;
[tex]cos(60) = \frac{1}{2}[/tex]
The cost price of a refridgator is $1850.00. A buyer who is given a discount of 5% for a cash purchase will pay
6( 5/12a− 5/18 )− 5/8 (4a+ 2/5 ) simplify
Answer:
think its 3a 3.83838
Step-by-step explanation:
Answer:
-23/11
Step-by-step explanation:
What is the slope of the line described by the equation y-1=3x
Answer:
Hey there!
The line can be expressed into y intercept form, y=3x+1.
Thus, in y=mx+b form, m is the slope, and we see that 3 is the slope of the line.
Let me know if this helps :)
boxes of raisins are labled as containing 22 ounces. Following are the weights, in the ounces, of a sample of 12 boxes. It is reasonable to assume that the population is approximatly normal.
21.88 21.76 22.14 21.63 21.81 22.12 21.97 21.57 21.75 21.96 22.20 21.80
Required:
Construct a 99% confidence interval for the mean weight.
Answer:
The 99 % confidence interval on the basis of mean is ( 21.7393 ; 22.0257)
Step-by-step explanation:
Mean = Sum of observations / Number of observations
Mean = 21.88 +21.76 +22.14 +21.63+ 21.81 +22.12+ 21.97+ 21.57+ 21.75+ 21.96 +22.20 +21.80/ 12
Mean =x`= 262.59/12= 21.8825
Standard Deviation = s= ∑x²/n - ( ∑x/n)²
∑x²/n= 478.7344 +473.4976 + 490.1796+467.8569+ 475.6761 + 489.2944+ 482.6809+ 465.2649+ 473.0625+ 482.2416 +492.84 + 475.24/ 12
∑x²/n= 5746.5689/12= 478.8807 = 478.881
Standard Deviation = s= ∑x²/n - ( ∑x/n)²
s= 478.881- (21.8825)²= 478.881-478.843= 0.037
The confidence limit 99% for the mean will be determined by
x` ± α(100-1) √s/n
Putting the values in the above equation
= 21.8825 ± 2.58 √0.037/12
Solving the square root
= 21.8825 ± 2.58 (0.05549)
Multiplying the square root with 2.58
=21.8825 ± 0.1432
Adding and subtracting would give
21.7393 ; 22.0257,
Hence the 99 % confidence interval on the basis of mean is ( 21.7393 ; 22.0257)
Jose added up his work hours for his paycheck. Last week he worked hours 25 5/8. This week he worked hours 32 5/6. How many total hours did he work in two weeks? with steps
Answer:
58 hours
Step-by-step explanation:
First week: 25 5/8 hours = 25 hrs 37 mins and 30 sec
Second weeK: 32 5/6 hrs = 32 hrs and 50 mins
To find the toal time in minutes
(37 + 50) mins = 1 hr 27 mins
Threfore, total number of hours he worked in two weeks:
(25 + 32 + 1) hrs = 58 hours
need help thankssssss
Answer:
301.44
Step-by-step explanation:
V=π r² h
V=π (4)² (12)
V= 603.19
divide by 2 to find half full: ≈ 301
301.44
What is the slope of the line that contains the points (2,5) and (4, - 3)?
Answer:
-4
Step-by-step explanation:
The slope would be (5 - (-3)) / (2 - 4) = 8 / -2 = -4.
Answer:
[tex]\huge\boxed{\text{The slope}\ m=-4}[/tex]
Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
(x₁; y₁), (x₂; y₂) - points on a line
We have the points:
[tex](2;\ 5)\to x_1=2;\ y_1=5\\(4;\ -3)\to x_2=4;\ y_2=-3[/tex]
Substitute:
[tex]m=\dfrac{-3-5}{4-2}=\dfrac{-8}{2}=-4[/tex]