Adam's cleats cost $65 and the sales tax is 5.5%. The sales tax amount is calculated by multiplying the price by the tax rate. The total cost is the sum of the initial price and the sales tax which is approximately $68.58.
Explanation:Adam is buying a new pair of baseball cleats for $65 and the sales tax is 5.5%. To find the total cost, we must find out the cost of the sales tax first. The sales tax can be calculated by multiplying the cost of the cleats by the sales tax percentage (in decimal form).
So, $65 * 0.055 = $3.575 is the tax amount. This means the sales tax on the cleats is $3.575.
The total cost Adam needs to pay is the sum of the cost of the cleats and the sales tax. Hence, $65 + $3.575 = $68.575. Therefore, the total cost that Adam will pay is approximately $68.58, because we usually round the money amount to the nearest cent.
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Could 1 2 . 2 cm , 6 . 0 cm , 12.2 cm,6.0 cm, and 4 . 2 cm 4.2 cm be the side lengths of a triangle?
Answer:
Yes they can be
According to the AAS corollary, which of the following sets of relationships can be used to show that VRT and STR are congruent?
A.STR VRT and VR ST
B. TVR SRT and VTR RTS
C. SRT VTR and VT SR
D. RST TVR and STR VRT
The AAS corollary from geometry states that two triangles are congruent if two angles and the non-included side of one triangle are equal to the two angles and the non-included side of another triangle. Because of this, option C is the correct answer as it confirms that triangles VRT and STR have these equal parts.
Explanation:The subject here is the Angle-Angle-Side (AAS) corollary in mathematics, specifically geometry. According to the AAS corollary, two triangles are congruent (identical in form) if two angles and the non-included side of one triangle are equal to the corresponding two angles and the non-included side of another triangle. Therefore, the set of relationships that confirm VRT and STR are congruent would be the one that shows that two angles and the non-included side in triangle VRT are equal to those in triangle STR.
Based on this, option C. SRT VTR and VT SR is the correct answer. It shows that angles SRT and VTR are equal (two angles) and sides VT and SR are equal (one side). Since the side (VT or SR) is not included between the two mentioned angles (SRT or VTR), this satisfies the conditions of the AAS corollary and can be used to show that triangles VRT and STR are congruent.
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The specifications for a new cardboard container require that the width for the container be 4 inches less than the length and the height be 1 inch less than twice the length.
a. Write a polynomial function that models the volume of the container in terms of its length.
b. Write an equation if the volume must be 2208 cubic inches.
c. Find the dimensions of the new container.
Answer:
c) Length = 12, width = 8 and height = 23.
Step-by-step explanation:
Let the length be x, then the width = x - 4 and the height = 2x - 1.
a) The polynomial is x(x - 4)(2x - 1)
b) x(x - 4)(2x - 1) = 2208
c) x(x - 4)(2x - 1) - 2280 = 0
2x^3 - 9x^2 + 4x - 2280 = 0
I'll use graphical software to find a solution for this. Its easily obtained online.
There is one real root and its x = 12.
So the dimensions of the box are L = 12, W = 8 and H = 23 inches.
Answer:
a) V(l)=2l³-9l²+4l
b) 2208=2l³-9l²+4l
c) 12in × 8in × 23in
Step-by-step explanation:
Got a 100% on edge 2020
there are 3 literature books, 4 algebra books, and 2 biology on a shelf. if a book is randomly selected, what is the probability of selecting a literature book or an algebra book?
Answer:
[tex]\frac{7}{9}[/tex]
Step-by-step explanation:
we know that
The probability of an event is the ratio of the size of the event space to the size of the sample space.
The size of the sample space is the total number of possible outcomes
The event space is the number of outcomes in the event you are interested in.
so
Let
x------> size of the event space
y-----> size of the sample space
so
[tex]P=\frac{x}{y}[/tex]
step 1
Find the probability of selecting a literature book
we have
[tex]x=3[/tex]
[tex]y=3+4+2=9[/tex]
substitute
[tex]P=\frac{3}{9}[/tex]
step 2
Find the probability of selecting an algebra book
we have
[tex]x=4[/tex]
[tex]y=3+4+2=9[/tex]
substitute
[tex]P=\frac{4}{9}[/tex]
step 3
Find the probability of selecting a literature book or an algebra book
Adds the probability of selecting a literature book plus the probability of selecting an algebra book
[tex]P=\frac{3}{9}+\frac{4}{9}=\frac{7}{9}[/tex]
Answer:
Step-by-step explanation:
Is it mutually exclusive?
Willis drove 239.82 miles in 4.2 hours at a constant speed. How long would it take him to drive 445.38 miles at the same speed?
Answer:
7.8 hours.
Step-by-step explanation:
We have been given that Willis drove 239.82 miles in 4.2 hours at a constant speed.
First of all let us find out speed at which Willis traveled 239.82 miles using speed formula.
[tex]\text{Speed}=\frac{\text{Distance}}{\text{Time}}[/tex]
[tex]\text{Speed}=\frac{239.82\text{ miles}}{4.2\text{ hours}}[/tex]
[tex]\text{Speed}=57.1\frac{\text{ miles}}{\text{ hour}}[/tex]
Now let us find time taken by Willis to cover a distance of 445.38 miles.
[tex]\text{Time}=\frac{\text{Distance}}{\text{Speed}}[/tex]
[tex]\text{Time}=\frac{445.38\text{ miles}}{57.1\frac{\text{ miles}}{\text{ hour}}}[/tex]
[tex]\text{Time}=\frac{445.38\text{ miles}}{57.1}\times\frac{\text{hour}}{\text{ miles}}}[/tex]
[tex]\text{Time}=\frac{445.38}{57.1}\times\text{hour}[/tex]
[tex]\text{Time}=7.8\text{ hour}[/tex]
Therefore, it will take Willis 7.8 hours to drive 445.38 miles at the same speed.
At a horse show, ribbons are awarded for first, second, third, and fourth places. There are 16 horses in the show. How many different arrangements of four horses are possible?
Answer:
43680 different arrangements are possible.
Step-by-step explanation:
The total number of horses are :16
We have to find different arrangement of four horses
Since, we have to find arrangements means we will use permutation
So, the required arrangement will be:
[tex]^{16}P_4[/tex]
Now, using: [tex]^{n}P_r=\frac{n!}{(n-r)!}[/tex]
Here, n= 16 and r=4 on substituting the values we get:
[tex]^{16}P_4=\frac{16!}{(16-4)!}[/tex]
[tex]\Rightarrow \frac{16!}{12!}[/tex]
[tex]\Rightarrow \frac{16\cdot 15\cdot 14\cdot 13\cdot 12!}{12!}[/tex]
Cancel out the common term that is 12! we get:
[tex]16\cdot 15\cdot 14\cdot 13[/tex]
After simplification we get: 43680
Hence, 43680 different arrangements are possible.
Roger has two golden retrievers, sadie and buddy, buddy weighs 14 pounds more than sadie, if their total wight is 136 pounds, how much does sadie weigh
Answer:
A) buddy = sadie + 14
B) buddy + sadie = 136
A) buddy -sadie = 14
Adding equations A & B
2 * buddy = 150
buddy = 75 pounds
sadie = 61 pounds
Step-by-step explanation:
If their total weight is 136 pounds, sadie weigh 61 pounds.
Let the weight of Sadie=x
Let the weight of Buddy=y
Hence:
y=x+14
Total weight= x +y=136 pounds
Formulate
14+2×x=136
x+x+14=136
2x=136-14
2x=122
Divide both side by 2x
x=122/2
x=61 pounds
Inconclusion If their total weight is 136 pounds, sadie weigh 61 pounds.
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True or False??
In the following number, the 8 is in the hundreds place.
15,829
Answer:
your answer is true.
Step-by-step explanation:
As 8 is in the hundredth place.
Answer:
The answer is True.
Step-by-step explanation:
9 is in the "ones place", 2 is in the "tens place, 8 is in the "hundreds place", and so on...
He surface area for a rectangular prism with a square base is SA=2s2+4sh. What is the surface area if s=2 and h=4?
Answer:
40 units²
Step-by-step explanation:
substitute the given values for s and h into the formula
SA = ( 2 × 2² ) + (4 × 2 × 4 ) = 8 + 32 = 40
Answer:
40 units²
Step-by-step explanation:
Given that the surface area for a rectangular prism with a square base is SA=2s2+4sh.
Where the values of the variables in the equation which are s and h are known, the area can be computed by the substitution of the known variables into the equation.
Hence where s = 2 and h = 4
SA = 2(2)² + 4(2)(4)
= 8 + 32
= 40 units²
AAHHH PLZ I HAVE 5 MIN LEFT!!!!
The sum of the measures of two angles of a scalene triangle is calculated, and the result is the same as the measure of one of the external angles of a triangle. Which pair of angle measures was calculated?
the remote interior angles
the adjacent interior angles
the adjacent interior angle and the larger remote interior angle
the adjacent interior angle and the smaller remote interior angle
Look at the triangle:
A right angle triangle is shown with hypotenuse equal to 17 centimeters. An acute angle of the triangle is labeled as x degrees
What is the value of cos x°? (1 point)
Select one:
a. 8 ÷ 17
b. 17 ÷ 8
c. 15 ÷ 17
d. 8 ÷ 15
In reference to the image below, the trigonometric ratio cos [tex]\alpha[/tex]° is calculated by dividing the base by the hypotenuse, thus making part c) 15 ÷ 17 the correct option.
The trigonometric ratios are six different proportions of the three sides of right angled triangle, namely, hypotenuse, perpendicular and base. The trigonometric ratios are sine, cosine, tan, sec, cosec and cot.
In the given question, the trigonometric ratio cos is given by dividing the base of the triangle to the hypotenuse.
In any question,
hypotenuse = side opposite of the right angle = 17
base = side adjacent to the acute angled marked = 15
Thus giving the value of cos [tex]\alpha[/tex]° as 15 ÷ 17.
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The complete question is given below:
A right angle triangle is shown with hypotenuse equal to 17 centimeters. An acute angle of the triangle is labeled as [tex]\alpha[/tex] degrees.
What is the value of cos [tex]\alpha[/tex]°?
a. 8 ÷ 17
b. 17 ÷ 8
c. 15 ÷ 17
d. 8 ÷ 15
The figure of triangle is given below:
Suppose we want a 90% confidence interval for the average amount spent on
entertainment (movies, concerts, dates, etc.) by Freshman in their first semester at a
large university. The interval is to have a margin of error of $2, and the amount spent
has a normal distribution with a standard deviation s = $30. The number of
observations required is closest to
A) 25.
B) 30.
C) 609.
D) 865.
A knitting machine used a total of 457,500 meters of yarn to make 100 cardigans and 200 pullovers yesterday. The machine takes the same length of yarn to make 21 pullovers as to make 20 cardigans.
What length of yarn does the machine use to make cardigans and pullovers?
The machine uses ______meters of yarn per cardigan and uses ______
meters per pullover.
Answer:
The machine uses 1575 meters of yarn per cardigan and uses 1500 meters per pullover.
Step-by-step explanation:
Let P be yarn needed by machine for each pullover and C be yarn needed by machine for each Cardigan.
We are told that the machine takes the same length of yarn to make 21 pullovers as to make 20 cardigans. We can represent this information as:
[tex]20C=21P...(1)[/tex]
The machine used a total of 457,500 meters of yarn to make 100 cardigans and 200 pullovers. We can represent this information as:
[tex]200P+100C=457,500...(2)[/tex]
Let us solve our system of equations using substitution method.
From equation (1) we will get,
[tex]C=\frac{21P}{20}[/tex]
Upon substituting this value in equation (2) we will get,
[tex]200P+100(\frac{21P}{20})=457,500[/tex]
[tex]200P+5*21P=457,500[/tex]
[tex]200P+105P=457,500[/tex]
[tex]305P=457,500[/tex]
[tex]P=\frac{457,500}{305}[/tex]
[tex]P=1500[/tex]
Therefore, the machine uses 1500 meters of yarn per pullover.
Upon substituting P=1500 in equation (1) we will get,
[tex]20C=21*1500[/tex]
[tex]20C=31,500[/tex]
[tex]C=\frac{31,500}{20}[/tex]
[tex]C=1575[/tex]
Therefore, machine uses 1575 meters of yarn per cardigan.
Answer:
1575 meters of yarn per cardigan
1500 meters per pullover
Step-by-step explanation:
Arrange the systems of equations that have a single solution in increasing order of x-values in their solutions. 2x+y=10
x-3y=-2
2x + y= 10
-6x -3y=-2
x+2y= 5
2x + y = 4
5x+ y= 33
x=18-4y
Y=13 -2x
8x + 4y =52
x+ 3y =5
6x-y=11
Y=10 + x
2x + 3y =45
Answer:
(III), (VI),(VII), (I), (IV)
Step-by-step explanation:
Solving the system of equations one by one by elimination method
(I) 2x+y=10
x-3y= -2 ( multiply by 2)
we have unique solution
x=4, y=2
(II) 2x+y=10 (multiply by -3)
-6x-3y= -2
No solution.
(III) x+2y=5 (multiply by 2)
2x+y=4
Unique solution
x=1, y=2
(IV) 5x+ y= 33
x=18-4y ---> x+4y=18 (multiply by 5)
Unique solution
x=6, y=3
(V) Y=13 -2x ----> 2x+y=13 ( multiply by 4)
8x + 4y =52
No solution
(VI) x+ 3y =5
6x-y=11 (multiply by 3)
Unique solution
x=2, y=1
(VII) Y=10 + x ----> -x+y=10 (multiply by 2)
2x + 3y =45
Unique solution
x=3 , y=13
Values of x in increasing order= (III), (VI),(VII), (I), (IV)
math help.......... will be marking brainly
Answer:
B.) 28%
Step-by-step explanation:
There are 50 total spins so far and 28% of them have been 4's. So that is the probability.
The amount of money Alan earns as a plumber after x hours is modeled by the equations y=25x + 50 what is the meaning of 25 in this models
Answer:
25 represents how much he makes per hour
Step-by-step explanation:
Please help!!! I only have three questions left!!!
A general proof for this would be that since Angle A + Angle F + Angle E = 180°, and each of these angles is congruent to some angle inside of Triangle CGH; that CGH would equal 180°.
Interior angles of triangles = 180°, which is common knowledge; unfortunately this isn't an answer choice - so we use the above proof.
F ~= C
A ~= H
E ~= G
So, Angles A and H are congruent would be the correct solution.
In the triangle below, what is cos B?
Answer:
[tex]\text{cos}(B)=\frac{c}{a}[/tex]
Step-by-step explanation:
We have been given a triangle. We are asked to find [tex]\text{cos}(B)[/tex].
We know that cosine relates adjacent side of a right triangle to its hypotenuse.
[tex]\text{cos}=\frac{\text{Adjacent}}{\text{Hypotenuse}}[/tex]
We can see that side AB is adjacent side and CB is hypotenuse of our given right triangle.
[tex]\text{cos}(B)=\frac{AB}{CB}[/tex]
[tex]\text{cos}(B)=\frac{c}{a}[/tex]
Therefore, our required value is [tex]\text{cos}(B)=\frac{c}{a}[/tex]
Your mom asked you to turn the oven down to 325 degrees. This is 75 degrees less than it was. What was the original temperature?
20. What is the determinant of B? {-18 3} {4 1}
Answer:
-30
Step-by-step explanation:
-18x1 - 4x3 = -18-12= -30
An electric filter purifies air at the rate of 35 liters per minute and uses energy at the rate of 0.8 Joules per minute. It also purifies water at the rate of 25 liters per minute and uses energy at the rate of 1.3 Joules per minute. The filter is expected to purify more than 1000 liters of air and water while using less than 170 Joules of energy. Let A denote the number of minutes it spends purifying air and W the number of minutes it spends purifying water.
Answer:
Write an inequality that represents the condition based on the number of liters of air and water.
35A+25W>1000
and the following inequality represents the condition based on the number of Joules of energy:
0.8A+1.3W<170
Step-by-step explanation:
Answer:
Step-by-step explanation:
I got it right on khan
What is an equation of the line, in point slope for, that passes though the given point and has the given slope? point:(7,3);slope:4/7
Answer:
The equation of this line is y - 3 = 4/7(x - 7)
Step-by-step explanation:
To find this, start with the base form of point-slope form.
y - y1 = m(x - x1)
Now put the slope in for m and the two coordinates in for (x1, y1).
y - 3 = 4/7(x - 7)
WILL MARK BRAINLEST PLS HELP
Which equation represents this ellipsis
A (x-2)^2 / 6^2 + (y-4)^2 /3^2 = 1
B(x-2)^2 / 12^2 + (y-4)^2 /6^2 = 1
C)(x-4)^2 / 6^2 + (y-2)^2 /3^2 = 1
D) (x-4)^2 / 12^2 + (y-2)^2 /6^2=1
Answer:
None
Step-by-step explanation:
The center of the ellipse is at (2, 4)
The length of the x axis is a= (8-2) =6
The length of the y axis is b=(16-4) = 12
The formula for an ellipse is
(x-h) ^2 (y-k)^2
----------- + -------------- = 1^2
a^2 b^2
where (h,k) is the center
and a and b are the lengths of the major and minor axes
(x-2) ^2 (y-4)^2
----------- + -------------- = 1
6^2 12^2
none of your choices have b>a and for the ellipse to be vertical b>a
Long division (4b^3+10b^2-32b+15) divided by (4b-6)
Answer:
4b^3 + 10b^2 - 32b + 15
___________________
2(2b - 3)
Step-by-step explanation:
Take out the greatest common factor of (4b - 6) which is 2 and 3.
Categorize the following polygon by the number of sides
heptagon
decagon
dodecagon
hexagon
Answer:
heptagon
Step-by-step explanation:
This polygon has 7 sides
heptagon is a seven sided polygon
decagon is a ten sided polygon
dodecagon is a 12 sided polygon
hexagon is a six sided polygon
Find (g - f)(x). f(x) = 1/x g(x) = x2 + 2x -5
A. 1/2-x^2-2x+5
B. 1/x+x^2+2x-5
C. x^2+2x-5-1/x
D. 1/x +x^2-5
Answer:
C) [tex]g(x)-f(x)=x^2 + 2x -5-\frac{1}{x}[/tex]
Step-by-step explanation:
[tex]f(x) = \frac{1}{x} \ g(x) = x^2 + 2x -5[/tex]
To find (g-f)(x) , we need to calculate g(x) - f(x)
WE know f(x) = 1/x and g(x) = x^2 + 2x -5
Plug in g(x) and f(x) and then subtract
[tex]g(x)-f(x)=x^2 + 2x -5- (\frac{1}{x})[/tex]
All are unlike terms so we cannot combine like terms
[tex]g(x)-f(x)=x^2 + 2x -5-\frac{1}{x}[/tex]
In order to find (g - f)(x), you need to subtract f(x) from g(x). The correct subtraction results in the expression x^2+2x-5-1/x, corresponding with answer choice C.
Explanation:The question asks you to calculate (g - f)(x) where f(x) = 1/x and g(x) = x^2 + 2x -5. This entails finding the difference between g(x) and f(x).
Firstly, write out g(x) and f(x):
g(x) = x^2 + 2x - 5f(x) = 1/xSecondly, subtract f(x) from g(x):
g(x) - f(x) = (x^2 + 2x - 5) - (1/x)
This simplifies to: g(x) - f(x) = x^2 + 2x - 5 - 1/x
Therefore, the correct answer is C. x^2+2x-5-1/x
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What is the asymptote of the graph of g(x)=3^x+6 ?
y=3
y=4
y=5
y=6
Answer:
y=6
Step-by-step explanation:
I took the test and got 100%
Y=7 and x= 6, perpendicular , parallel or neither?
Answer:
I think the answer is neither. Hope this helps.
Step-by-step explanation:
There are 8 blue marbles and 7 red marbles in a bag. Julie pulls two marbles at random from the bag first. What is the probability that she first pulls a blue marble and then a red marble?
Answer:
either a ratio 8;7. or a percentage of 53% for picking the blue marble first i think and a 50/50 chance if you keep that blue marble out.
Step-by-step explanation:
Answer: [tex]\frac{4}{15}[/tex]
Step-by-step explanation:
Given: Number of blue marbles = 8
Number of red marbles = 7
Total number of marbles = 8+7=15
Now, the probability that she first pulls a blue marble is given by :-
[tex]P(B)=\frac{\text{blue marbles}}{\text{Total marbles}}\\\\=\frac{8}{15}[/tex]
Now, total marbles left in bag = 15-1=14
Now, the probability that she second pulls a red marble is given by :-
[tex]P(B)=\frac{\text{red marbles}}{\text{Total marbles left}}\\\\=\frac{7}{14}=\frac{1}{2}[/tex]
Thus, the probability that she first pulls a blue marble and then a red marble is given by :-
[tex]P(B)\timesP(R)=\frac{8}{15}\times\frac{1}{2}=\frac{4}{15}[/tex]
Omar has a new credit card. He earns 300 reward points for every 100 dollars he spends. If Omar earned 1800 reward points, how much money did he spend?
Answer:
He earned 1800 reward points for 600 dollars
Step-by-step explanation:
Given the statement: Omar has a new credit card. He earns 300 reward points for every 100 dollars he spends. If Omar earned 1800 reward points.
Unit rate are expressed as a quantity of 1, such as 3 feet per second or 4 miles per hour, they are called unit rates.
Earn 300 reward point for every 100 dollars.
⇒ unit rate per reward = [tex]\frac{100}{300}[/tex] dollars
we have to find how many dollars he earned for 1800 points.
[tex]Number of dollars = unit rate \times 1800[/tex]
= [tex]\frac{100}{300} \times 1800 = 600[/tex]
Therefore, he earned 1800 reward points for 600 dollars
Answer:
$600 money Omar spends .
Step-by-step explanation:
As given
Omar has a new credit card.
He earns 300 reward points for every 100 dollars he spends.
i.e
300 reward points for every 100 dollars .
Let us assume that the Omar earned 1800 reward points when he spends x money.
Than the equation becomes
[tex]x = \frac{1800\times 100}{300}[/tex]
[tex]x = \frac{1800}{3}[/tex]
x = $600
Therefore $600 money Omar spends .