A pair of children shoes comes in a box that measures 10.2 cm x 15 cm x 8 cm what is the volume of a shoebox A pair of children shoes comes in a box that measures 10.2 cm x 15 cm x 8 cm what is the volume of a shoebox
Answer:
1224 cm^3
Step-by-step explanation:
The shape of the box is a rectangular prism.
The volume of a rectangular prism is given by the formula below.
volume = length * width * height
volume = 10.2 cm * 15 cm * 8 cm
volume = 1224 cm^3
Final answer:
The volume of a shoebox with dimensions 10.2 cm x 15 cm x 8 cm is calculated by multiplying these three dimensions together, resulting in a volume of 1224 cm³.
Explanation:
To calculate the volume of a shoebox, you multiply its length by its width by its height. For a shoebox with dimensions of 10.2 cm, 15 cm, and 8 cm, the calculation would look like this:
Volume = Length × Width × Height
Volume = 10.2 cm × 15 cm × 8 cm
Volume = 1224 cm³
Therefore, the volume of the shoebox is 1224 cubic centimeters.
A smart-phone is thrown upwards from the top of a 448-foot building with an initial velocity of 48 feet per second. The height h of the smart-phone after t seconds is given by the quadratic equation h = − 16 t 2 + 48 t + 448 h=-16t2+48t+448. When will the smart-phone hit the ground?
Answer:
The smart-phone hit the ground when t = 7 s
Step-by-step explanation:
The height "h" is defined as:
h=16t^2 + 48t + 448
And, when the smart-phone hits the ground, h = 0 ft . Then,
16t^2 + 48t + 448 = 0
And this is a quadratic equation, and we can solve it using the formula for ax^2 + bx + c = 0, which is
x=[tex]\frac{-b±\sqrt{b^{2}-4ac } }{2a}[/tex]
So,
t = [tex]\frac{-48±\sqrt{48^{2} -4(-16)(448)} }{2(16)}[/tex]
t = [tex]\frac{-48±\sqrt{2304+28672} }{-32}[/tex]
And, we have two responses,
t_1 = [tex]\frac{-48+\sqrt{30976} }{-32}[/tex] and t_2 = [tex]\frac{-48-\sqrt{30976} }{-32}[/tex]
t_1 = - 4 s and t_2 = 7 s
As we know, the time is a quantity that cannot have a negative value, so, we take the result 2.
Final answer:
The smart-phone will hit the ground after approximately 3 seconds.
Explanation:
To find when the smart-phone will hit the ground, we need to determine the value of t that makes h equal to zero in the quadratic equation h = -16t^2 + 48t + 448. This equation represents the height h of the smart-phone after t seconds. To solve the equation, we can use the quadratic formula t = (-b ± sqrt(b^2 - 4ac)) / (2a). Plugging in the values a = -16, b = 48, and c = 448, we can solve for t. The positive value of t will give us the time it takes for the smart-phone to hit the ground.
Step-by-step solution:
Substitute the values a = -16, b = 48, and c = 448 into the quadratic formula: t = (-48 ± sqrt(48^2 - 4*(-16)*448)) / (2*(-16))
Simplify the expression inside the square root: t = (-48 ± sqrt(2304 + 28672)) / (-32)
Simplify further: t = (-48 ± sqrt(30976)) / (-32)
Calculate the square root of 30976: t = (-48 ± 176) / (-32)
Determine the values of t: t = (-48 + 176) / (-32) = 3 or t = (-48 - 176) / (-32) = -5
Choose the positive value t = 3 since we are interested in the time it takes for the smart-phone to hit the ground
Therefore, the smart-phone will hit the ground after approximately 3 seconds.
#10 FIND X, Y, AND Z!
WILL GIVE BRANLIEST
Answer:
25/6
Step-by-step explanation:
Because the line in the middle is an angle bisector, 5*10 = 12*x.
This means that 50 =12x, so 25/6 = x
A student wants to know how his IQ of 160 stacks up with the population. Using your knowledge of IQ scores (mean=100, SD=15), how many standard deviations is his IQ score above the mean?
The standard deviation is his IQ score above the mean is found by the Z score whose value is 4.
What is the standard deviation?It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.
[tex]\rm \sigma = \sqrt{\dfrac{ \sum (x_i-X)}{n}[/tex]
σ is the standard deviation
xi is each value from the data set
X is the mean of the data set
n is the number of observations in the data set.
It is given that,
Sample average, x = 160
mean, [tex]\mu[/tex] = 100
Standard deviation, [tex]\sigma =[/tex] 15
The Z-test value is found as,
[tex]\rm Z = \frac{x- \mu}{\sigma} \\\\ Z = \frac{160-100}{15} \\\\ Z = 4[/tex]
Thus, the standard deviation is his IQ score above the mean is found by the Z score whose value is 4.
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A student with an IQ score of 160 is 4 standard deviations above the mean IQ of 100 according to the given normal distribution, where one standard deviation equals 15 points.
To calculate how many standard deviations a score is above or below the mean, you can use the formula:
Z = (X - x) / SD
Where:
Z is the Z-score, which indicates the number of standard deviations a data point is from the mean.X is the data pointx is the mean of the distributionSD is the standard deviationApplying this to the student's IQ score:
Z = (160 - 100) / 15
Z = 60 / 15
Z = 4
Therefore, a student with an IQ score of 160 is 4 standard deviations above the mean IQ, which is considered exceptionally high.
Tom is in dire need of a new washing machine. He knows what model he would like to get, but doesn't have the cash to pay for it. He plans to get a line of credit (credit card) at the store when he purchases his new washer. He found four different stores that carry the same washing machine for different prices. The lines of credit they offer also come with different APRs. Tom's primary goal is to minimize his monthly payment as he pays the washing machine off over the next 18 months. From which of the four stores should Tom purchase his washing machine? a. Bob's Nuts and Bolts b. Steve's Scratch and Dent c. Wally's Washing Machines d. Al's Appliances Please select the best answer from the choices provided A B C D
Answer:
b. Steve's Scratch and Dent.
Step-by-step explanation:
Tom should purchase his washing machine from Steve's Scratch and Dent.
At a banquet, the ratio of the number of boys to the number of girls is 5 : 3. 20 boys leave and the ratio becomes 5 : 4. How many girls are at the banquet?
Answer:
There are 48 girls at the banquet
Step-by-step explanation:
Let the number of boys =x
Let the number of girls=y
Ratio Of boys to girls=5:3
Therefore, x:y=5:3......(1)
If 20 boys leave, the ratio becomes 5:4
Sine number of boys=x
If 20 boys leave, new number = x-20
Therefore, x-20:y=5:4......(2)
From (1),
3x=5y
From Equation (2),
4(x-20)=5y
Therefore: 3x=4x-80
x=80
From (1),
3x=5y
5y=3X80
y=240/5=48
Therefore, there are 48 girls at the banquet
What does the Principle of Superposition tell us about relative ages of the strata in the cross-sections you were looking at? Older rocks might be found on top of younger rocks-what could cause that? Why is an igneous intrusion younger than the rocks it’s found in?
Answer:
1. The Principle of superposition states that a strata of rock is younger than the one over which it is laid.
2. The intrusion of the younger rock by the principle of cross-cutting relationship
3. The intrusion igneous rock arrived after the rock it is found in had already been in place and is stable.
Step-by-step explanation:
In geology, the Principle of superposition states that, in its originally laid down state, a strata sequence consists of older rocks over which younger rocks are laid. That is, a stratum of rock is younger than the stratum upon which it rests.
The principle of cross cutting relationships in a geologic intrusion occurrence, the feature which intrudes or cut across another feature is always than the feature it cuts across.
The reason is that based on the geologic time frame, the rock 1 which ws cut across by rock 2 was already in the geologic zone in a more steady state than rock , therefore it is older than the cutting rock 2.
45 percent of all customers who enter a store will make a purchase. Suppose that 6 customers enter the store and that these customers make independent purchase decisions.
The solution is in the attachment
Write 3.45 as a reduced mixed number.
Answer:
3 [tex]\frac{9}{20}[/tex]
Step-by-step explanation:
3.45=3 45/100
reduce and divided by 5
3 45/100= 3 9/20
Answer:
Step-by-step explanation:
add me on fortnite
Can someone please actually help me with this?
Images Below
Answer:
65
62
Step-by-step explanation:
In inscribed quadrilaterals, opposite angles are supplementary.
First problem:
x + 148 = 180
x = 32
2x + 1 = 65
Second problem:
x + 20 + 3x = 180
x = 40
180 − (2x + 38) = 62
HELP !
10 POINTS & BRANLIEST
Answer:
Name the congruent triangles:
triangle RWS, triangle SWT, and triangle TSR
Polygon ABCDE is an irregular pentagon. Find the perimeter of the polygon. Round to the nearest tenth. Round to give final answer only.
Answer:
12.9
Step-by-step explanation:
AB = [tex]\sqrt{2^{2}+3^{2} }[/tex] = [tex]\sqrt{13}[/tex]
BC = [tex]\sqrt{2^{2}+2^{2} }[/tex] = [tex]2\sqrt{2}[/tex]
CD = [tex]\sqrt{1^{2}+2^{2} }[/tex] = [tex]\sqrt{5}[/tex]
DE = 3
EA = [tex]\sqrt{1^{2} + 2^{2} }[/tex] = [tex]\sqrt{5}[/tex]
The sum of all of these (in decimal form) is (approx.) 12.9
Answer:
13.9 units
Step-by-step explanation:
AB = sqrt(2² + 3²) = sqrt(13)
BC = sqrt(2² + 2² = sqrt(8)
CD = sqrt(1² + 2²) = sqrt(5)
DE = 3
EA = sqrt(1² + 2²) = sqrt(5)
Add all these:
13.9 units
A fire engine starts pumping water at 9:20 am at the rate of 800 gallons per minute. Another fire engine, pumping at the rate of 1000 gallons per minute, starts at 9:30 am. At what time will the two engines have pumped the same number of gallon
Answer:
10:10 AM
Step-by-step explanation:
The first thing is to use an identical time variable for both cases, we will do it as follows:
Let t = number of minutes of pumping time of the first fire engine
Therefore, for the second fire truck it would be:
(t-10) = pumping time of the second fire engine, since it started 10 min after the first engine.
To find the value of t, we equalize the equations of the first engine and the second engine:
We know that the first one would be: 800 * t
And the second: 1000 * (t-10)
Thus
1000 * (t-10) = 800 * t
1000 * t - 10000 = 800t
1000 * t - 800 * t = 10000
200 * t = 10000
t = 10000/200
t = 50 minutes
In other words, 50 minutes after the first engine starts pumping, it equaled the second
To know the time they were matched it would be like this:
9:20 AM +: 50 = 10:10 AM
Therefore, at 10:10 AM both engines were matched.
To check the above we have to:
50 * 800 = 40000
40 * 1000 = 40000
Therefore, in that time, they were equalized.
Answer:
At 10:10 am
Step-by-step explanation:
Hi to answer this question we have to write a system of equations:
Fire engine 1: 800 mWhere m: pumping time of the engine
Fire engine 2: 1000 (m-10)Because it starts 10 minute later
So, putting together both equations:
800m = 1000(m-10)
800m = 1000m - 10000
10000 = 1000m-800m
10000= 200m
10000/200=m
50 =m (50 minutes after the first engine starts)
So, 9:20 am + 50 minutes : 10:10 am .
The solution set for -18 < 5x - 3 is _____.
-3 < x
3 < x
-3 > x
3 > x
Solution set for given inequality [tex]-18 < 5x - 3[/tex] is [tex]-3 < x[/tex].
What is solution set?" Solution set is defined as the such set of values which satisfies the given equation or any inequality."
According to the question,
Given inequality,
[tex]-18 < 5x - 3[/tex]
Add 3 both the side of inequality we get,
[tex]-18 +3 < 5x - 3 +3[/tex]
[tex]= -15 < 5x[/tex]
Divide both the side by 5 to get the solution set ,
[tex]-3 < x[/tex]
Hence, solution set for given inequality [tex]-18 < 5x - 3[/tex] is [tex]-3 < x[/tex].
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Final answer:
The solution set for the inequality -18 < 5x - 3 is -3 < x, after adding 3 to both sides and then dividing by 5.
Explanation:
The student has asked to find the solution set for the inequality -18 < 5x - 3. To solve this, we first isolate the variable x by adding 3 to both sides of the inequality:
-18 + 3 < 5x - 3 + 3
-15 < 5x
Then, we divide both sides by 5 to solve for x:
-15 / 5 < 5x / 5
-3 < x
This simplifies to the inequality x > -3, which means that the correct answer is: -3 < x.
Abraham throws a ball from a point 40 m above the ground. The height of the ball from the ground level after ‘t' seconds is defined by the function h(t) = 40t – 5t2. How long will the ball take to hit the ground?
Answer:
8.899s
Solve: -5t^+40t+40
4-2√2 is the time taken by the ball to hit the ground.
What is Distance?Distance is the total movement of an object without any regard to direction
Given that Abraham throws a ball from a point 40 m above the ground. The height of the ball from the ground level after ‘t' seconds is defined by the function h(t) = 40t – 5t². then we need to find the time for ball to hit the ground.
The given function is
h(t)=40t-5t²
Let h(t)=40
We get,
40t-5t²=40
5t²-40t+40=0
t²-8t+8=0
(t-4)²=8
t-4=±√8
t=±√8+4
t=√8+4; t=4-√8
By considering the reality we know t>0
t=4-2√2
Hence t=4-2√2 is the time taken by the ball to hit the ground.
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Joan is building a sandbox in the shape of a regular pentagon. The perimeter of the pentagon is 35y4 – 65x3 inches. What is the length of one side of the sandbox? 5y – 9 inches 5y4 – 9x3 inches 7y – 13 inches 7y4 – 13x3 inches
Answer:
Step-by-step explanation:
given that Joan is building a sandbox in the shape of a regular pentagon.
The perimeter of the pentagon is
[tex]35y^4 - 65x^3[/tex]inches.
Since regular pentagon we know that all sides are equal and there are totally five sides.
Perimeter of regular pentagon = 5*side
= 5a where a = length of side
Equate 5a to given perimeter to get
[tex]5a=35y^4 - 65x^3\\[/tex]
divide by 5
[tex]a=\frac{35y^4 - 65x^3}{5} \\=7y^4-13x^3[/tex]
Answer:
D. 7y^4 - 13x^3 inches
Combined with the equation −9x + 3y = 12 creates a system of linear equations with no solution? Select one: A. 18x - 6y = 20 B. 3x - y = -4 C. -16x + 9y = 30 D. 5x + 8y = -1
Answer:
The correct option is A. 18x - 6y = 20
Step-by-step explanation:
A system of two equations has no solution if the lines having these equations are parallel to each other.
Also, two lines [tex]a_1x+b_1y=c_1[/tex] and [tex]a_2x+b_2y=c_2[/tex] are parallel,
If [tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq \frac{c_1}{c_2}[/tex]
While,
They coincide ( infinitely many solution ) if [tex]\frac{a_1}{a_2}=\frac{ b_1}{b_2}=\frac{c_1}{c_2}[/tex],
They are non parallel ( a unique solution ) if [tex]\frac{a_1}{a_2}\neq \frac{ b_1}{b_2}\neq \frac{c_1}{c_2}[/tex],
Here, the given equation,
-9x + 3y = 12
Since in lines -9x + 3y = 12 and 18x - 6y = 20,
[tex]\frac{-9}{18}=\frac{3}{-6}\neq \frac{12}{20}[/tex]
Hence, system −9x + 3y = 12, 18x - 6y = 20 has no solution.
In lines -9x + 3y = 12 and 3x - y = -4,
[tex]\frac{-9}{3}=\frac{3}{-1}= \frac{12}{-4}[/tex]
Hence, system −9x + 3y = 12, 3x - y = -4 has infinitely many solutions.
In lines -9x + 3y = 12 and -16x + 9y = 30 ,
[tex]\frac{-9}{-16}\neq \frac{3}{9}\neq \frac{12}{30}[/tex]
Hence, system −9x + 3y = 12, -16x + 9y = 30 has a solution.
In lines -9x + 3y = 12 and 5x + 8y = -1,
[tex]\frac{-9}{5}\neq \frac{3}{8}\neq \frac{12}{-1}[/tex]
Hence, system −9x + 3y = 12, 5x + 8y = -1 has a solution.
Factor the expression.
6n3 + 8n2 + 3n + 4
A. (2n2 + 1)(3n + 4)
B. (2n2 – 1)(3n + 4)
Answer:
The answer to your question is letter A
Step-by-step explanation:
Data
Factor 6n³ + 8n² + 3 n + 4
- To factor this expression, factor the common terms of the first two factors
6n³ + 8n² = 2n²(3n + 4)
- Factor 1 in the second two terms 1(3n + 4)
- Factor all the expression by like terms 2n²(3n + 4) + 1(3n + 4)
(3n + 4)(2n² + 1)
3 freshmen and 2 sophomores from a sorority will attend a conference. If the sorority has 12 freshmen and 9 sophomores, in how many different ways can the conference attendees be selected?
Answer:
7920
Step-by-step explanation:
12C3 × 9C2
= 220×36
= 7920
The number of different ways the conference attendees be selected is 7920 ways
What are Combinations?
The number of ways of selecting r objects from n unlike objects is:
ⁿCₓ = n! / ( ( n - x )! x! )
Given data ,
The number of fresher men in sorority = 12 fresher men
The number of sophomores in sorority = 9 sophomores
In the conference ,
The number of fresher men from sorority =3 fresher men
The number of sophomores from sorority = 2 sophomores
To calculate the number of different ways the conference attendees be selected is by using combination
So , the combination will become
Selecting 3 fresher men from 12 and selecting 2 sophomores from 9
And , the equation for combination is
ⁿCₓ = n! / ( ( n - x )! x! )
The combination is ¹²C₃ x ⁹P₂
¹²C₃ x ⁹P₂ = 12! / ( 9! 3! ) x 9! / ( 7! 2! )
= ( 12 x 11 x 10 ) / ( 3 x 2 ) x ( 9 x 8 ) / 2
= 1320 / 6 x 72 / 2
= 220 x 36
= 7920 ways
Hence , the number of different ways the conference attendees be selected is 7920 ways
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A circle in the xyxyx, y-plane has its center at the point (-6,1)(−6,1)(, minus, 6, comma, 1, ). If the point (7,12)(7,12)(, 7, comma, 12, )lies on the circle, what is the radius of the circle? Round the answer to the nearest tenth.
Answer:
r=17.0
Step-by-step explanation:
In a circle with center (h,k) and any point (x,y) on the circle, the radius of the circle is given as:
[tex](x -h)^2 + (y - k)^2 =r^2[/tex]
Center (h,k)=(-6,1)
(x,y)=(7,12)
[tex]r^2=(x -h)^2 + (y - k)^2 \\r^2=(7 -(-6))^2 + (12 - 1)^2\\r^2=(7 +6)^2 + 11^2\\r^2=13^2 + 11^2=169+121=290\\r=\sqrt{290}=17.03[/tex]
radius, r=17.0 (to the nearest tenth)
The radius of the circle with center (-6,1) and passing through the point (7,12) can be found using the distance formula. The radius, or distance between these two points, calculates to approximately 17.0 units when rounded to the nearest tenth.
Explanation:In Mathematics, you can determine the radius of a circle if you have the coordinates of the center and a point on the circle. Here, we have the center of the circle at (-6,1) and a point (7,12) lying on the circle. We will use the distance formula to find the radius, r, which is essentially the distance between these two points.
Distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
By substituting the given points into the distance formula, we get
Radius (r) = sqrt((7 - (-6))^2 + (12 - 1)^2)
Sample calculation: r = sqrt((7 - (-6))^2 + (12 - 1)^2) = sqrt(169 + 121) = sqrt(290). Therefore, the radius of the circle, rounded to the nearest tenth, is approximately 17.0 units.
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an equilateral triangle has an area of 25 √3 cm squared. what is the height
5 √ 3 c m
A t = √ 34 * s 2 = 25 √ 3
this makes the sides 10cm
At= 1/2 b * h
25 √ 3 = 12 ⋅ 10 ⋅ h = 5 √ 3 c m
Answer:
Height = 8.66 cm
Step-by-step explanation:
The formula for the area of an equilateral triangle is expressed as
A = S²√3/4,
where s represents the length of each side. The area of the given equilateral triangle is 25 √3 cm squared. Therefore
25 √3 = S²√3/4
Dividing both sides of the equation by √3, it becomes
25 √3/√3 = S²√3/4√3
25 = S²/4
Cross multiplying, it becomes
S² = 25 × 4 = 100
Taking square root of both sides of the equation, it becomes
√S² = √ 100
S = 10 cm
In an equilateral triangle, all the sides are equal. The height of the equilateral triangle divides it into two equal right angles triangle. The angles in each right angle triangle are 90, 60 and 30 degrees. To determine the height, h, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
10² = h² + 5²
100 = h² + 25
h² = 100 - 25 = 75
h = √75
h = 8.66 cm
I don’t know how to find the surface area?
Answer:
Step-by-step explanation:
its just writing teh answwer out and then solving
Answer:
The surface area of a prism is the sum of the areas of the 6 faces. That will be
the 2 squares and the other 4 rectangles.
S=2*(b*h)+4(B*H)
b and h are base and height of the squares and B and H of the Rectangles.
b=2
h=2
B=5
H=2
so
S=2*(2*2)+4(2*5)=8+40=48
A can in the shape of a right circular cylinder is required to have a volume of 500 cubic centimeters. The top and bottom are made of a material that costs 11 cents per square centimeter, while the sides are made of a material that costs 8 cents per square centimeter. Express the total cost C of the material as a function of the radius r of the cylinder.
Answer:
The answer to the question is
The total cost C of the material as a function of the radius r of the cylinder is
0.6912·r² + 800/r Dollars.
Step-by-step explanation:
To solve the question, we note that
The area of the top and bottom combined = 2·π·r²
The area of the sides = 2·π·r·h
and the volume = πr²h = 500 cm²
Therefore height = 500/(πr²)
Substituting the value of h into the area of the side we have
Area of the side = 2πr·500/(πr²) = 1000/r
Therefore total area of can = Area of top + Area of bottom + Area of side
Whereby the cost of the can = 0.11×Area of top +0.11×Area of bottom +0.8×Area of side
Which is equal to
0.11×2×π×r²+ 0.8×1000/r = 0.6912·r² + 800/r
The cost of the can is $(0.6912·r² + 800/r)
To express the cost of the cylinder's material as a function of its radius, we first find the expression for the cylinder's height using the volume formula. The total cost C is computed by calculating the expenses for the top, bottom, and sides of the cylinder using their respective costs and surface areas. These give the final expression for the cost C(r)= 22πr^2 + 8000/r.
Explanation:Given that the volume of the right circular cylinder is 500 cubic centimeters, we can first use the formula for the volume of a cylinder, which is V=πr2h, where r is the radius of the base and h is the height of the cylinder. This can be rearranged to solve for h, giving us h=V/(πr2).
Next, the total cost C is given by the cost of the materials for the top, bottom, and sides of the cylinder: C= 2(11πr2)+ (8 * 2π*r*h). Plugging the expression h= 500/(πr2) into the cost function gives us: C = 22πr2 + (16πr * 500/r2), which simplifies to: C = 22πr2 + 8000/r. So, the total cost of the material as a function of the radius r of the cylinder is C(r)= 22πr2 + 8000/r.
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A company has 8 cars and 11 trucks.The state inspector will select 3 cars and 4 trucks to be tested for safety inspections in how many ways can this be done
Answer:
Number of ways to select 3 cars and 4 trucks = 18,480
Step-by-step explanation:
Let x be the number of ways to select 3 cars and 4 truck.
Given:
Total number of cars = 8
Total number of Trucks = 11
We need to find out how many ways can the inspector select 3 cars and 4 truck.
Solution:
Using combination formula.
[tex]nCr = \frac{n!}{r!(n-r)!}[/tex]
Where, n = Total number of object.
m = Number of selected object.
We need to find out how many ways can the inspector select 3 cars and 4 truck from 8 cars and 11 trucks.
So, we write the the combination as given below.
[tex]8C_{3}\times 11C_{4} = Number\ of\ ways\ to\ selection[/tex]
[tex]\frac{8!}{3!(8-3)!} \times \frac{11!}{4!(11-4)!}= x[/tex]
[tex]x = \frac{8\times 7\times 6\times 5!}{3!\times 5!} \times \frac{11\times 10\times 9\times 8\times 7!}{4!\times 7!}[/tex]
Factorial 5 and 7 is cancelled.
[tex]x = \frac{8\times 7\times 6}{6} \times \frac{11\times 10\times 9\times 8}{24}[/tex] ([tex]3! = 6\ and\ 4! = 24[/tex])
[tex]x = (8\times 7) \times (11\times 10\times 3)[/tex] ([tex]\frac{9\times 8}{24}=\frac{72}{24}=3[/tex])
[tex]x=56\times 330[/tex]
x = 18480
Therefore, the Inspector can select 3 cars and 4 trucks in 18,480 ways,
To determine how many ways the state inspector can select 3 cars from 8 and 4 trucks from 11, we need to calculate the combinations separately for each type of vehicle and then multiply them together to find the total number of ways to make both selections simultaneously.
### Selection of Cars:
The number of ways to choose 3 cars from 8 is a combination problem, because the order in which we select the cars does not matter. The formula for combinations, denoted as C(n, k), where n is the total number of items to choose from, and k is the number of items to be chosen, is given by:
C(n, k) = n! / (k! * (n - k)!)
Let's apply this formula to select 3 cars from 8:
C(8, 3) = 8! / (3! * (8 - 3)!) = 8! / (3! * 5!) = (8 × 7 × 6) / (3 × 2 × 1)
Simplify the factorials by canceling out common terms:
C(8, 3) = (8 × 7 × 6) / (3 × 2 × 1) = (8/2) × (7/1) × (6/3) = 4 × 7 × 2 = 56
So, there are 56 ways to choose 3 cars out of 8.
### Selection of Trucks:
Similarly, to choose 4 trucks out of 11 we use the combination formula again:
C(11, 4) = 11! / (4! * (11 - 4)!) = 11! / (4! * 7!) = (11 × 10 × 9 × 8) / (4 × 3 × 2 × 1)
Simplify the factorials:
C(11, 4) = (11 × 10 × 9 × 8) / (4 × 3 × 2 × 1) = (11/1) × (10/2) × (9/3) × (8/4) = 11 × 5 × 3 × 2 = 330
So, there are 330 ways to choose 4 trucks out of 11.
### Total Ways:
To find the total number of ways to select both the cars and trucks for inspection, we multiply the number of ways to choose the cars by the number of ways to choose the trucks:
Total number of ways = number of ways to choose cars × number of ways to choose trucks
Total number of ways = 56 (from choosing cars) × 330 (from choosing trucks)
Total number of ways = 56 × 330 = 18480
Therefore, the state inspector can select 3 cars out of 8 and 4 trucks out of 11 in 18,480 different ways.
-2/x^2-4 + x-1/x^2-2x
1. Identify the type of problem
2. Think of how to do this problem
3. Do the Work
4. Answer
Answer:
I need help with this too
Step-by-step explanation:
A family has a rectangular back yard that measures 5x+4 by 3x-2 they are building a square patio with side lengths that measure x+3. write an expression for the area of grass that will be left in the back yard after the patio is built. show your work.
Answer: 14x² - 4x - 17
Step-by-step explanation:
The formula for determining the area of a rectangle is expressed as
Area = length × width
The rectangular back yard measures 5x + 4 by 3x - 2. This means that the area of the rectangular back yard would be
Area = (5x + 4)(3x - 2)
Area = 15x² - 10x + 12x - 8
= 15x² + 2x - 8
The formula for determining the area of a square is expressed as
Area = length²
Length of square patio = x + 3
Area of square patio = (x + 3)(x + 3)
= x² + 3x + 3x + 9
= x² + 6x + 9
The expression for the area of grass that will be left in the back yard after the patio is built is
15x² + 2x - 8 - (x² + 6x + 9)
= 15x² + 2x - 8 - x² - 6x - 9
= 15x² - x² + 2x - 6x - 8 - 9
= 14x² - 4x - 17
The sample consisted of 50 night students, with a sample mean GPA of 3.02 and a standard deviation of 0.08, and 25 day students, with a sample mean GPA of 3.04 and a standard deviation of 0.06. The test statistic is:
Answer: The test statistic is t= -0.90.
Step-by-step explanation:
Since we have given that
n₁ = 50
n₂ = 25
[tex]\bar{x_1}=3.02\\\\\bar{x_2}=3.04\\\\\sigma_1=0.08\\\\\sigma_2=0.06[/tex]
So, s would be
[tex]s=\sqrt{\dfrac{n_1\sigma_1^2+n_2\sigma_2^2}{n_1+n_2-2}}\\\\s=\sqrt{\dfrac{50\times 0.08^2+25\times 0.06^2}{50+25-2}}\\\\s=0.075[/tex]
So, the value of test statistic would be
[tex]t=\dfrac{\bar{x_1}-\bar{x_2}}{s(\dfrac{1}{n_1}+\dfrac{1}{n_2})}\\t=\dfrac{3.02-3.04}{0.074(\dfrac{1}{50}+\dfrac{1}{25})}\\\\t=\dfrac{-0.04}{0.074(0.02+0.04)}\\\\t=\dfrac{-0.04}{0.044}\\\\t=-0.90[/tex]
Hence, the test statistic is t= -0.90.
Here are summary statistics for randomly selected weights of newborn girls: nequals177, x overbarequals28.9 hg, sequals6.7 hg. Construct a confidence interval estimate of the mean. Use a 98% confidence level. Are these results very different from the confidence interval 28.1 hgless thanmuless than30.7 hg with only 20 sample values, x overbarequals29.4 hg, and sequals2.3 hg? What is the confidence interval for the population mean mu?
Answer:
(32.2,34.7)
Step-by-step explanation:
Solution :
Given that,
\bar x = 33.4 hg
s = 6.4 hg
n = 177
Degrees of freedom = df = n - 1 = 177 - 1 = 176
At 99% confidence level the t is ,
α = 1 - 99% = 1 - 0.99 = 0.01
α / 2 = 0.01 / 2 = 0.005
tα /2,df = t0.005,176 = 2.604
Margin of error = E = tα/2,df * (s /√n)
= 2.604* ( 6.4/ √177)
= 1.25
The 95% confidence interval estimate of the population mean is,
\bar x - E < \mu < \bar x + E = 33.4 - 1.25 < \mu < 33.4 + 1.25
32.15 < \mu < 34.65
32.2 < \mu < 34.7
(32.2,34.7)
Question:
Here are summary statistics for randomly selected weights of newborn girls: n = 177, x = 28.9 hg, s = 6.7 hg. Construct a confidence interval estimate of the mean. Use a 98% confidence level. Are these results very different from the confidence interval 28.1 hg < μ < 30.7 hg with only 20 sample values, x' =29.4 hg, and s = 2.3 hg? What is the confidence interval for the population mean μ?
Answer:
The confidence interval for the population mean μ is 27.73 ≤ μ ≤ 30.0714
Step-by-step explanation:
The equation to identify the confidence interval for the mean is given by
[tex]x'-z_{\frac{\alpha }{2}} \frac{s}{\sqrt{n} } \leq \mu\leq x'+z_{\frac{\alpha }{2}} \frac{s}{\sqrt{n} }[/tex]
Where
x' = Sample mean = 28.9
s = Standard deviation = 6.7
n = Sample size = 177
[tex]z_{\frac{\alpha }{2}}[/tex] = Critical value = 2.326
Therefore we have
[tex]28.9-2.326\frac{6.7}{\sqrt{177} } \leq \mu\leq 28.9+2.326 \frac{6.7}{\sqrt{177} }[/tex]
27.73 ≤ μ ≤ 30.0714
T test we have
t = [tex]\frac{x'-\mu}{\frac{s}{\sqrt{n} } }[/tex]
=[tex]\frac{29.4-28.9}{\frac{2.3}{\sqrt{16} } }[/tex] = 0.8696 which is < 1
df = 15 as sample size = 15
Upper tail statistics lies between 0.3 and 0.1
Eli made fancy blue costume decorations for each of the dancers in his year-end dance performance.He used 1/10 of a meter of ribbon for each decoration,which he got by cutting 1/5 of a meter of ribbon into equal pieces. How many decorations did Eli make?
Answer: There are 2 decorations that Eli makes.
Step-by-step explanation:
Since we have given that
Length of a meter of ribbon used = [tex]\dfrac{1}{10}=\dfrac{1}{10}\times 100=10[/tex]
Length of a meter cut into equal pieces = [tex]\dfrac{1}{5}=\dfrac{1}{5}\times 100=20[/tex]
So, Number of decorations that Eli make is given by
[tex]\dfrac{\text{Length of total ribbon}}{\text{Length of ribbon used}}\\\\=\dfrac{20}{10}\\\\=2[/tex]
Hence, there are 2 decorations that Eli makes.
Final answer:
Eli made 2 decorations from 1/5 meter of ribbon by using 1/10 meter of ribbon for each decoration.
Explanation:
Eli made fancy blue costume decorations for each dancer in his year-end dance performance.
Eli used 1/10 of a meter of ribbon for each decoration and initially cut a 1/5 meter ribbon into equal pieces.
To calculate the number of decorations Eli made, we need to divide the length of ribbon he cut (1/5 meter) by the length of ribbon used for each decoration (1/10 meter).
To solve this, we simply perform the division:
= 1/5 meter / 1/10 meter
= 2.
Therefore, Eli made 2 decorations from 1/5 meter of ribbon.
Walt made an extra $7000 last year from a part-time job. He invested part of the money at 3% and the rest at 3.25%. He made a total of $220.00 in interest. How much was invested at 3.25%?
A $4000
B $3000
C $5000
D $3500
Answer: A $4000
Step-by-step explanation:
Let x represent the amount which he invested at 3% interest.
Let y represent the amount which he invested at 3.25% interest.
Walt made an extra $7000 last year from a part-time job. He invested part of the money at 3% and the rest at 3.25%. This means that
x + y = 7000
The formula for determining simple interest is expressed as
I = PRT/100
Considering the account paying 3% interest,
P = $x
T = 1 year
R = 3℅
I = (x × 3 × 1)/100 = 0.03x
Considering the account paying 3.25% interest,
P = $y
T = 1 year
R = 3.25℅
I = (y × 3.25 × 1)/100 = 0.0325y
He made a total of $220.00 in interest., it means that
0.03x + 0.0325y = 220 - - - - - - - -- -1
Substituting x = 7000 - y into equation 1, it becomes
0.03(7000- y) + 0.0325y = 220
210 - 0.03y + 0.0325y = 220
- 0.03y + 0.0325y = 220 - 210
0.0025y = 10
y = 10/0.0025
y = 4000