Answer:
19 in × 4 inStep-by-step explanation:
l - length
w - width
The formula of a perimeter of a rectangle: P = 2(l + w)
The formula of an area of a rectangle: A = lw
We have P = 46in and A = 76in² Substitute:
(1) 2(l + w) = 46
(2) lw = 76
2(l + w) = 46 divide both sides by 2
l + w = 23 subtract w from both sides
l = 23 - w
subtitute it to (2):
(23 - w)w = 76 use the distributive property
23w - w² = 76 subtract 76 from both sides
-w² + 23w - 76 = 0 change the signs
w² - 23w + 76 = 0
w² - 4w - 19w + 76 = 0
w(w - 4) - 19(w - 4) = 0
(w - 4)(w - 19) = 0 ⇔ w - 4 = 0 or w - 19 = 0
w - 4 = 0 add 4 to both sides
w = 4
w - 19 = 0 add 19 to both sides
w = 19
Put the values of w to (1):
l = 23 - 4 = 19 or l = 23 - 19 = 4
You can work no more than 60 hours each week at your two jobs. Dog walking pays $7 per hour and your sales job at Computers & More, Inc. pays $12 per hour. You need to earn at least $450 each week to pay your bills. Your friend solves the system of inequalities and tells you that a possible solution is (-3, 50). Is this a possible solution, why or why not?
Answer:
No
Step-by-step explanation:
You cannot work negative 3 hours, it's impossible. One possible solution would be to work 50 hours a week at dog walking for 7 dollars an hour, and 10 hours a week at Computers & More, Inc. for 12 dollars a week. This would give you 350 dollars from dog walking, and 120 dollars from Computers & More, Inc. This would be a total of 470 dollars.
Answer:
No, this is not a possible solution because it does not satisfy all inequalities of the system.
Step-by-step explanation:
Let x represents the number of hours spent on dog walking and y represents the number of hours spent on sales job at Computers & More Inc.,
Given,
Total hours can not be no more than 60 hours,
⇒ x + y ≤ 60
Dog walking pays $7 per hour and your sales job at Computers & More, Inc. pays $12 per hour.
Thus, the total earning = 7x + 12y
According to the question,
Total earning ≥ $ 450
⇒ 7x + 12y ≥ 450
Also, hours can not be negative,
⇒ x ≥ 0; y ≥ 0
Hence, the system of inequalities that shows the given situation is,
7x + 12y ≥ 450;
x + y ≤ 60;
x ≥ 0; y ≥ 0
Since, -3 ≥ 0 ( False ),
Thus, the point is not satisfying all inequalities of the system,
Hence, it can not be the solution.
Please help me out with this
Answer:
76.9 in²
Step-by-step explanation:
The area (A) of any sector in a circle is
A = area of circle × fraction of circle
= πr² × [tex]\frac{77}{360}[/tex]
= π × 10.7² × [tex]\frac{77}{360}[/tex]
= [tex]\frac{10.7^2(77)\pi }{360}[/tex] ≈ 76.9 in²
To rent a carpet cleaner at the hardware store, there is a set fee and an hourly rate. The rental cost, c, can be determined using this equation
when the carpet cleaner is rented for h hours
c = 25 + 3h
Which of these is the hourly rate?
A.3
B.3h
C.25
D.25h
3h
The set cost is 25, because c=25 when h=0. So, this leaves 3h as the hourly rate.
The hourly rate of the carpet cleaning is specified correctly by: Option A: 3
How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
c = rental cost of a carpet cleaner
h = number of hours the carpet cleaner is rented.
c = 25 + 3h can be written as:
c = 25 + (3+3+3+...+3) (h times)
That shows that 3 is added h times, which is the number of hours, so for each 1 of h hours, there is one 3 added in the final rental cost. (assuming nothing complex is going to happen)
That shows that the hourly rate is 3.
Thus, the hourly rate of the carpet cleaning is specified correctly by: Option A: 3
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Decima is a spanish song form that is a style of poetry. how many lines does it have?
The spanish song Decima has ten lines
Final answer:
A decima is a Spanish form of poetry that consists of ten lines per stanza, with a fixed rhyme pattern of ABBAACCDDC, representing a distinct structure from other forms like sonnets or haikus.
Explanation:
The decima is a form of Spanish poetry. Unlike a sonnet, which typically comprises fourteen lines and may follow various rhyme schemes such as the Shakespearian or Petrarchan forms, the decima is characterized by its ten-line stanzas. These stanzas adhere to a specific rhyme pattern and are traditionally written in eight-syllable lines. Each line in a decima ends with a rhyme following the pattern ABBAACCDDC. The form is quite popular in Spanish literature and folk music, and it is distinct in its total line count from other forms like the sonnet, sestina, and haiku.
June has 42 sports books, 85 mystery books, and 69 nature books. She arranged her books equally on 7 shelves. How many books are on each shelf.
Answer:
28
Step-by-step explanation:
Add 42, 85, and 69 together and you get 196 but you need to divide that by 7 and you get 28
Answer:
28
Step-by-step explanation:
We are given that
June has sports books=42
June has mystery books=85
June has nature books=69
Total number of shelves=7
We have to find the number of books are on each shelf.
Total number of books=42+85+69=196
To find the number of books on each shelf we will divide the total number of books by 7.
Number of books on each shelf=[tex]\frac{196}{7}[/tex]
Number of books on each shelf=28
Hence, number of books on each shelf=28
Please help me with this
Answer:
8 ft
Step-by-step explanation:
The area (A) of a triangle = [tex]\frac{1}{2}[/tex] bh
where b is the base and h the perpendicular height
Using b = 20 and h = 12, then
A = 0.5 × 20 × 12 = 120 ft²
Using b = 30 and perpendicular height = h, then
0.5 × 30 × h = 120
15h = 120 ( divide both sides by 15
h = 8
According to lots of Pythagorean theorem,
h=7
I really don’t want to show my work because it took a while to solve this lol but if you want me to show my work just comment
If set A = {3, 4, 7, 9}, set B = {8, 9, 10, 11}, and set C = {4, 9, 11, 13, 15}, then A∩(B∪C) =
{}
{4, 9}
{3, 4, 7, 9, 11}
A = {3, 4, 7, 9}
B = {8, 9, 10, 11}
C = {4, 9, 11, 13, 15}
A∩(B∪C)
First let's solve parentheses, we want the union between B and C.
B∪C = {4, 8, 9, 10, 11, 13, 15}
Now we want the interception between A and this, which means we want just the value which appears in both.
A∩{4, 8, 9, 10, 11, 13, 15} = {4, 9}
Final answer:
To determine A∩(B∪C), first calculate the union of B and C which is {4, 8, 9, 10, 11, 13, 15}. Then find the intersection of this union with set A, which results in {4, 9}.
Explanation:
To find the intersection of set A with the union of sets B and C, denoted as A∩(B∪C), we first identify the union of sets B and C. The union of two sets contains all elements that are members of either set, without duplicates. Therefore, the union of set B = {8, 9, 10, 11} and set C = {4, 9, 11, 13, 15} is the set that contains all distinct elements from both, which is {4, 8, 9, 10, 11, 13, 15}.
Next, we identify the intersection of set A with this union. The intersection of two sets contains only the elements that are members of both sets. Set A = {3, 4, 7, 9}. We check which elements in set A are also in the union of B and C. The elements 4 and 9 appear in both set A and the union of B and C. Consequently, the intersection A∩(B∪C) is {4, 9}.
The number 0.9967 represents the area under the standard normal curve below a particular z-score.
What is the z-score?
Enter your answer, as a decimal to the nearest hundredth, in the box.
Answer:
2.72
Step-by-step explanation:
Here, we use a z-score table or calculator to look up the probability and find the corresponding z-score.
P(z < ?) = 0.9967 at z = 2.72.
Using the normal distribution principle, the Zscore which corresponds to the area under the normal curve at P(Z < z) = 0.9967 is 2.716
To obtain the Zscore in this scenario, which is the number of standard deviations from the mean value for a given score ; we make use of Zscore calculator or a normal distribution table ;
Using a normal distribution table;
Zscore at P(Z < z) = 0.9967 is 2.716Therefore, the Zscore value is 2.716
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The function [tex]f(x)=3x^3+x^2+2x[/tex] rises as x grows very large.
A. True
B. False
Answer:
A. True
Step-by-step explanation:
The given function is;
[tex]f(x)=3x^3+x^2+2x[/tex]
The leading coefficient of this polynomial function is positive.
The degree of the polynomial is odd.
This implies that, the function will rise on the left and keep rising on the right.
Hence, the end behavior of the function tells us that, the function rises as x-values grow very large.
The correct option is True
Emanuel surveyed a random sample of 50 subscribers to Auto Wheel magazine about the number of cars that they own. Of the subscribers surveyed, 15 own fewer than 2 vehicles. There are 340 subscribers to Auto Wheel magazine. Based on the data, what is the most reasonable estimate for the number of Auto Wheel magazine subscribers who own fewer than 2 vehicles?
PLEASE
Answer:
The most reasonable estimate for the number of Auto Wheel magazine subscribers who own fewer than 2 vehicles is 102.
Step-by-step explanation:
Consider the provided information.
A random sample of 50 subscribers to Auto Wheel magazine about the number of cars that they own. Of the subscribers surveyed, 15 own fewer than 2 vehicles.
We need to find the most reasonable estimate for the number of Auto Wheel magazine subscribers who own fewer than 2 vehicles if there are 340 subscribers.
Here, the sample used is 50 and the population size is 340.
Now use the formula to find the reasonable estimate.
[tex]\frac{Part}{Sample}=\frac{x}{Population}[/tex]
Substitute the respective values in the above formula as shown;
[tex]\frac{15}{50}=\frac{x}{340}[/tex]
[tex]\frac{15}{50}\times 340=x[/tex]
[tex]x=3\times 34[/tex]
[tex]x=102[/tex]
Hence, the most reasonable estimate for the number of Auto Wheel magazine subscribers who own fewer than 2 vehicles is 102.
WILL GIVE BRAINLIEST
Answer:
(x,y) --> (x, y-5)
Step-by-step explanation:
the y-intercept of f(x) = (0,2)
the y-intercept of g(x) = (0, -3)
-3 - 2 = -5
Please help will give brainliest thank you.
Two events are dependent if the outcome of the first event affects the outcome of the second.
The last answer is the correct one.
Which description means the same as the limit expression? (Image attached)
A. The graph falls on the left side.
B. The graph rises on the left side.
C. The graph falls on the right side.
D. The graph rises on the right side.
Answer:
B. The graph rises on the left side.
Step-by-step explanation:
The limit provided on the image is interpreted as; The limit of the function f(x) as x approaches negative infinity is infinity.
X is approaching negative infinity, this means that along the x-axis we are moving towards the left where the values of x become increasingly negative.
On the other hand, f(x) is approaching positive infinity, meaning that along the y-axis we are moving upwards where the values of y become increasingly positive.
This typically implies that as we move towards the left the graph of f(x) is moving upwards or basically the graph rises on the left side.
Answer:
b. the graph rises on the left side
Please help me out!!!
Answer:
y = 30.
Step-by-step explanation:
As they are similar corresponding sides are in the same ratio.
So (y + 20) / 20 = 100/40
(y + 20) / 20 = 5/2
2(y + 20) = 5*20
y + 20 = 50
y = 30 (answer).
The Flat Rock auto assembly plant in Detroit, Michigan, produces three different makes of automobiles. In two years, the plant constructed a total of 390,000 cars. If 90,000 more cars were made in the first year than in the second year, how many cars were made in each year?
a. first year: 90,000
second year: 180,000
b. first year: 300,000
second year: 90,000
c. first year: 240,000
second year: 150,000
d. first year: 180,000
second year: 90,000
Answer:
c. first year: 240,000
second year: 150,000
Step-by-step explanation:
We let the number of cars made in the second year be X. Consequently, the number of cars made in the first year would be X+90000 since we are told that 90,000 more cars were made in the first year than in the second year. Furthermore, we are also told that the total number of cars constructed in these two years is 390,000, implying that;
X+X+90000=390000
2X+90000=390000
2X=390000-90000
2X=300000
X=150000; number of cars made in second year
The number made in the first year is thus;
150000+90000 = 240000
Answer:
Option c is correct
So, the cars made in 1st year = x = 240,000
and the cars made in 2nd year = 150,000
Step-by-step explanation:
in this question we have to find the number of cars made in each year by The Flat Rock auto assembly plant.
Given:
the plant constructed a total of 390,000 cars and 90,000 more cars were made in the first year than in the second year
Let cars made in 1st year = x
and cars made in 2nd year = y
then the plant constructed a total of 390,000 will be :
x+ y = 390,000 (i)
and
90,000 more cars were made in the first year than in the second year can be written as:
x=90,000 +y (ii)
Solving equation (i) and (ii) we can find the values of x and y
Putting value of x from eq (ii) into eq(i)
(90,000 + y) + y = 390,000
90,000 +y +y =390,000
2y = 390,000 - 90,000
2y= 300,000
y= 150,000
Putting value of y in equation (ii) we can find the value of x
x= 90,000 + y
x= 90,000 + 150,000
x= 240,000
So, the cars made in 1st year = x = 240,000
and the cars made in 2nd year = 150,000.
Given the ordered pair P(1, -3), determine the requested secant, cosecant, or cotangent of angle ?. Cot ? = _____
[tex]\bf P(\stackrel{x}{1},\stackrel{y}{-3})\qquad \qquad cot(\theta )=\cfrac{\stackrel{\stackrel{adjacent}{x}}{1}}{\stackrel{\stackrel{opposite}{y}}{-3}}[/tex]
The value of Cotangent or cot is: [tex]cot \;\theta= \frac{1}{-3}[/tex]
What are Trigonometric ratios?Trigonometric ratios are the ratios of the length of sides of a triangle.
In trigonometry, there are six trigonometric ratios, namely, sine, cosine, tangent, secant, cosecant, and cotangent.
Given ordered pair P(1, -3).
As we know that Cotangent is ratio of base : perpendicular i.e.,
adjacent of x: opposite y
So, [tex]cot \;\theta= \frac{1}{-3}[/tex]
Now, Hypotenuse = [tex]\sqrt{base^{2}+perpendicular^{2} }[/tex]
= [tex]\sqrt{1^{2} + (-3)^{2}} =\sqrt{10}[/tex]
and,
[tex]sec\;\theta= \frac{\sqrt{10} }{1} \\cosec\;\theta =\frac{\sqrt{10} }{(-3)}[/tex]
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Joe ran 3 miles yesterday and wanted to run at least 12 miles this week. Write an inequality that can be used to determine the additional number of days joe must run this week if each run is 3 miles. Then solve the inequality .
Answer:
if you take into consideration the run from yesterday,
Joe needs to run at least three more days
y > = 3
if you don't take into consideration the 3 mile run from yesterday,
The answer is
He needs to run 4 or more days toachieve his goal
y > = 4
Step-by-step explanation:
12 miles as a minimum
that means
let x be the total amount of miles ran
x > = 12
Let y be the number of days in which Joe runs
3*y > = 12
y > = 4
Joe needs to run for at least 3 more days to meet his goal of running at least 12 miles this week, considering that each run is 3 miles.
We can set up an inequality. Joe has already run 3 miles, so we need to find out how many more miles he needs to run. If Joe runs 3 miles each day, the inequality representing the situation is 3d + 3 \\geq 12, where d is the number of additional days Joe must run.
We can solve the inequality as follows:
Subtract 3 from both sides of the inequality: 3d \\geq 9.Divide both sides by 3: d \\geq 3.This means Joe needs to run for at least 3 more days to meet his goal of 12 miles.
in the triangle determine the value of c
Answer: The answer is A: 8.6
Step-by-step explanation: In this case, the side you're trying to figure out is the opposite and the side measurement given is the hypotenuse.
This means that out of the sin, cos, and tan we will be using sin.
Sin(Ф)= opposite/hypotenuse
Plug in the numbers you know: Sin(35)=x/15
Take the 15 to the other side to get x by itself
Then plug into your calculator 15Sin(35)=x
This gives you 8.6
If a(x) = 3x + 1 and 5(x)=1/x-4, what is the domain of (ba)(x)?
For this case we have the following fusions:
[tex]a (x) = 3x + 1\\b (x) = \frac {1} {x} -4[/tex]
We must find [tex](a * b) (x):[/tex]
By definition:
[tex](a * b) (x) = a (x) * b (x)\\(a * b) (x) = (3x + 1) * (\frac {1} {x} -4)\\(a * b) (x) = \frac {3x} {x} -12x + \frac {1} {x} -4\\(a * b) (x) = 3-12x + \frac {1} {x} -4\\(a * b) (x) = - 12x + \frac {1} {x} -1[/tex]
The domain of the function will be given by all the values for which the function is defined, that is, all real numbers except zero.
Answer:
(-∞, 0) U (0,∞)
if f(x)=8x+7 and g(x)=x+2 what is (f*g)(2)
Answer:
92
Step-by-step explanation:
Assuming your (f*g)(2) is the product f(2)*g(2), you have ...
f(2) = 8*2 +7 = 23
g(2) = 2+2 = 4
(f*g)(2) = f(2)*g(2) = 23*4 = 92
Answer:
Step-by-step explanation:23
What is the 6th value in the sequence with the explicit formula
an= −2n−14?
Answer:
a6 = -26
Step-by-step explanation:
Fill in n=6 and do the arithmetic.
a6 = -2·6 -14 = -12-14 = -26
Solution:
Given, Tn = -2n - 14
To Find : What is the 6th value in the sequence
Solution: Simply Substitute the value of n as 6 .
Tn = -2n-14
Tn = -2(6) -14
Tn = -12 - 14
Tn = -14 - 12
Tn = -26
Therefore -10 is the 6th value in the sequence.
(05.06)
Choose the graph below that represents the following system of inequalities: (1 point)
y ≥ −3x + 1
y ≤ 1 over 2 x + 3
Answer:
The second graph represents the system of inequalities
[tex]y\geq-3x + 1\\\\y\leq\frac{1}{2}x + 3\\[/tex]
Step-by-step explanation:
Let us first consider how the graphs of the inequalities will look like.
For the inequality [tex]y\geq-3x + 1[/tex] all the values "above" the line [tex]y=-3x + 1[/tex] are its solutions (because of the [tex]\geq[/tex] sign).
And for the inequality [tex]y\leq\frac{1}{2}x + 3[/tex] all the values the "below" the line [tex]y=\frac{1}{2}x + 3[/tex] are its solutions (because of the [tex]\leq[/tex] sign).
Together these system of inequalities have the solutions as shown in the second figure.
Answer:
The second graph.
Yr Welcome
Step-by-step explanation:
Use the divergence theorem to evaluate the integral i = z z ∂w f · ds when f(x, y, z) = y i − 4yz j + 3z 2 k and ∂w is the boundary of the solid w enclosed by the upper half of the sphere
[tex]\vec f(x,y,z)=y\,\vec\imath-4yz\,\vec\jmath+3z^2\,\vec k[/tex]
[tex]\implies\nabla\cdot\vec f(x,y,z)=0-4z+6z=2z[/tex]
By the divergence theorem,
[tex]\displaystyle\iint_{\partial W}\vec f\cdot\mathrm d\vec S=\iiint_W2z\,\mathrm dV[/tex]
I'll assume a sphere of radius [tex]r[/tex] centered at the origin, and that [tex]W[/tex] is bounded below by the plane [tex]z=0[/tex]. Convert to spherical coordinates, taking
[tex]x=\rho\cos\theta\sin\varphi[/tex]
[tex]y=\rho\sin\theta\sin\varphi[/tex]
[tex]z=\rho\cos\varphi[/tex]
Then
[tex]\displaystyle\iiint_W2z\,\mathrm dV=\int_0^{\pi/2}\int_0^{2\pi}\int_0^r2\rho^3\cos\varphi\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=\pi r^4[/tex]
Final answer:
The given question involves using the divergence theorem to evaluate an integral involving a vector field and a surface. The vector field is given as f(x, y, z) = y i - 4yz j + 3z^2 k and the surface of interest is the upper half of a sphere.
Explanation:
The given question involves using the divergence theorem to evaluate an integral involving a vector field and a surface. The vector field is given as f(x, y, z) = y i - 4yz j + 3z^2 k and the surface of interest is the upper half of a sphere.
To solve this, we need to apply the divergence theorem, which states that the integral of the divergence of a vector field over a closed surface is equal to the triple integral of the divergence of the vector field over the volume enclosed by that surface. In this case, the volume is the upper half of the sphere and the divergence of the vector field is div(f) = ∂f/∂x + ∂f/∂y + ∂f/∂z.
By evaluating the divergence of the vector field and simplifying the expression, we can then use the divergence theorem to convert the surface integral into a volume integral, which can be evaluated using appropriate coordinates.
Which of the following is csc(-166°) equal to?
csc(14°)
-csc(14°)
-csc(-14°)
csc(166°)
Answer:
-csc(14°)
Step-by-step explanation:
The given trigonometric expression is csc(-166°)
-166° is in the third quadrant.
It makes an angle of 14° with the x-axis.
Hence the principal angle for -166° is 14°
In the third quadrant the cosecant function is negative.
This implies that;
csc(-166°) =-csc(14°)
The correct choice is the second option.
Charles went to a restaurant for dinner and paid a tip of 15% on the total bill amount. He then had an ice cream that cost $13 less than the total restaurant bill excluding the tip.
If he spent $43 in all, how much was the total restaurant bill excluding the tip?
A.
$13.95
B.
$26.05
C.
$48.69
D.
$24.89
Answer:
B. $26.05
Step-by-step explanation:
Since this was a multiple choice question, I used process of elimination. I got rid of A because $13.95 - the ice cream ($13) would be no where near $43. For B, i did ($26.05) + ($26.05 - $13) which equals $39.10 and then i did ($39.10 + ($26.06 x 0.15) and that gave me $43 in all.
The quotient of three divided by the sum of two and four
The sum is the answer to an addition problem. 2+4=6. so, 3÷6=0.5
The quotient of three divided by the sum of two and four will be 0.5.
What is a number system?The number system is a way to represent or express numbers.
Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.
Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.
As per the given,
Three divided by the sum of two and four
3/(2 + 4) = 3/6 = 0.5
Hence "The quotient of three divided by the sum of two and four will be 0.5".
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I need to find the surface area and volume of all three figures. If you could provide what equations you used to I will be grateful :)
Thank you <3
Answer:
Part 1) Sphere The surface area is equal to [tex]SA=196\pi\ m^{2}[/tex] and the volume is equal to [tex]V=\frac{1,372}{3}\pi\ m^{3}[/tex]
Part 2) Cone The surface area is equal to [tex]SA=(16+4\sqrt{65})\pi\ units^{2}[/tex] and the volume is equal to [tex]V=\frac{112}{3}\pi\ units^{3}[/tex]
Part 3) Triangular Prism The surface area is equal to [tex]SA=51.57\ mm^{2}[/tex] and the volume is equal to [tex]V=17.388\ mm^{3}[/tex]
Step-by-step explanation:
Part 1) The figure is a sphere
a) Find the surface area
The surface area of the sphere is equal to
[tex]SA=4\pi r^{2}[/tex]
we have
[tex]r=14/2=7\ m[/tex] ----> the radius is half the diameter
substitute
[tex]SA=4\pi (7)^{2}[/tex]
[tex]SA=196\pi\ m^{2}[/tex]
b) Find the volume
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]r=14/2=7\ m[/tex] ----> the radius is half the diameter
substitute
[tex]V=\frac{4}{3}\pi (7)^{3}[/tex]
[tex]V=\frac{1,372}{3}\pi\ m^{3}[/tex]
Part 2) The figure is a cone
a) Find the surface area
The surface area of a cone is equal to
[tex]SA=\pi r^{2} +\pi rl[/tex]
we have
[tex]r=4\ units[/tex]
[tex]h=7\ units[/tex]
Applying Pythagoras Theorem find the value of l (slant height)
[tex]l^{2}=r^{2} +h^{2}[/tex]
substitute the values
[tex]l^{2}=4^{2} +7^{2}[/tex]
[tex]l^{2}=65[/tex]
[tex]l=\sqrt{65}\ units[/tex]
so
[tex]SA=\pi (4)^{2} +\pi (4)(\sqrt{65})[/tex]
[tex]SA=16\pi +4\sqrt{65}\pi[/tex]
[tex]SA=(16+4\sqrt{65})\pi\ units^{2}[/tex]
b) Find the volume
The volume of a cone is equal to
[tex]V=\frac{1}{3}\pi r^{2}h[/tex]
we have
[tex]r=4\ units[/tex]
[tex]h=7\ units[/tex]
substitute
[tex]V=\frac{1}{3}\pi (4)^{2}(7)[/tex]
[tex]V=\frac{112}{3}\pi\ units^{3}[/tex]
Part 3) The figure is a triangular prism
a) The surface area of the triangular prism is equal to
[tex]SA=2B+PL[/tex]
where
B is the area of the triangular base
P is the perimeter of the triangular base
L is the length of the prism
Find the area of the base B
[tex]B=\frac{1}{2} (2.7)(2.3)=3.105\ mm^{2}[/tex]
Find the perimeter of the base P
[tex]P=2.7*3=8.1\ mm[/tex]
we have
[tex]L=5.6\ mm[/tex]
substitute the values
[tex]SA=2(3.105)+(8.1)(5.6)=51.57\ mm^{2}[/tex]
b) Find the volume
The volume of the triangular prism is equal to
[tex]V=BL[/tex]
where
B is the area of the triangular base
L is the length of the prism
we have
[tex]B=3.105\ mm^{2}[/tex]
[tex]L=5.6\ mm[/tex]
substitute
[tex]V=(3.105)(5.6)=17.388\ mm^{3}[/tex]
The probability that Carmen will get an A on her math test is 80%, and the probability that she will get an A on her science test is 60%.
What is the probability that she will get an A on both tests? Express your answer as a decimal rounded to the nearest hundredth.
Answer:
70%
Step-by-step explanation:
60+80=140
140/2=70
f(x)=2x^2-3x+9
what is f(3)
Answer:
when x=3, the answer is
f(3)=36
Step-by-step explanation:
You need to plug in 3 for x and then solve. :)
Hope this helps! If possible, could you please mark as brainliest? Thanks!
Answer:
18
Step-by-step explanation:
Wherever you put a 3 in for the x's that are on the right.
f(x) = 2x^2 - 3x + 9
f(3) = 2*3^2 - 3(3) + 9
f(3) = 2*9 - 9 + 9
f(3) = 18
Jason and Beth are married and don’t have any kids yet. They are out of debt except for their house, and they have a full emergency fund. But Beth’s car has sputtered its last breath. Fortunately, she’s found a new one for hundreds less than invoice. The payments will be less than a fourth of their combined take- home pay. This fits Dave’s formula, and the payments can be squeezed into their budget. She’ll take $2,000 out of their emergency fund for the down payment. Jason thinks it’s a really bad idea. Why?
Final answer:
Jason thinks it's a bad idea to use the emergency fund for a car down payment as it should be reserved for unforeseen financial emergencies, not planned expenses like a vehicle purchase.
Explanation:
Jason may consider it a bad idea for Beth to use the emergency fund for a down payment on a car because the emergency fund is supposed to be a safety net for unforeseen and critical financial needs, such as sudden medical expenses, job loss, or urgent home repairs.
Depleting the emergency fund for a car purchase, despite the fact that car payments are affordable, puts them at risk should multiple unplanned expenses arise simultaneously.
Financial advisers often recommend keeping 3-6 months of expenses saved for emergencies to maintain financial security. Therefore, it might be better to save up for the down payment separately or consider a less expensive car.
Final answer:
Jason may be concerned about using the emergency fund for a car downpayment since emergency funds are meant for unforeseen and urgent financial needs. Adding new debt could make them vulnerable to financial strain.
Explanation:
The concern Jason may have with Beth taking $2,000 out of their emergency fund for a down payment on a new car is that the emergency fund should be reserved for unforeseen circumstances, such as medical expenses, unexpected home repairs, or job loss. Using it for a car down payment, even if it seems manageable within their budget, could leave them vulnerable if a real emergency arises. Additionally, even though the car payments fit within Dave Ramsey's guidelines of being less than a quarter of their take-home pay, it introduces new debt—which they have worked hard to eliminate, except for their mortgage—and could potentially add financial strain if their income situation changes.