Answer:
58.6667
Step-by-step explanation:
if you see there are 5280 ft in 1 mile so use ur brain
Answer:
58.67 feet per second.
Step-by-step explanation:
We have been given that Jackrabbit are capable of reaching speeds up to 40 miles per hour. We are asked to represent this speed in feet per second.
We know that 1 mile equals 5280 feet.
We also know that 1 hour equals 3600 seconds.
[tex]\text{Speed of jackrabbit}=\frac{\text{40 miles}}{\text{Hour}}\times \frac{\text{5280 feet}}{\text{Mile}}\times \frac{\text{1 hour}}{\text{3600 sec}}[/tex]
[tex]\text{Speed of jackrabbit}=\frac{40 \times\text{5280 feet}}{\text{3600 sec}}[/tex]
[tex]\text{Speed of jackrabbit}=\frac{211200\text{ feet}}{\text{3600 sec}}[/tex]
[tex]\text{Speed of jackrabbit}=\frac{58.67\text{ feet}}{\text{3600 sec}}[/tex]
Therefore, the speed of jackrabbit is 58.67 feet per second.
Let x represent the number of small candle. let y represent the number the number of large candles.
A small candle costs $2.25and a large candle cost 4.75 Jerome cannot spend more than $80. write an inequality that models the amount spent on small and large candles
Answer:
The inequality that models the situation is [tex]2.25x+4.75y \leq 80[/tex]
Step-by-step explanation:
Let
x ----> represent the number of small candles
y ----> represent the number of large candles
we know that
The inequality that represent this situation is equal to
[tex]2.25x+4.75y \leq 80[/tex]
using a graphing tool
The solution is the shaded triangular area, because the number of candles cannot be a negative number
see the attached figure
Factor completely x2 − 10x + 25. (2 points)
Answer:
(x-5)(x-5)
Step-by-step explanation:
Ok... This ones actually pretty simple.
So all you have to do is find 2 numbers that add up to -10, and multiply to 25. You will quickly realize that the only 2 numbers that do that are -5 and -5. Then, all you have to do is write the now factored equation. (x-5)(x-5)
There are 2 ways to check your work. The first is to FOIL (first, inside, outside, last). This should get you back to your original equation
The second way to do it is to plug it into a graphing program. If you graph your factored equation and your original equation, they should be the same!
I hope this helps!
If you have any other questions just feel free to ask me.
For this case we must factor the following expression:
[tex]x ^ 2-10x + 25[/tex]
For this, we must find two numbers that when multiplied give 25 and when added to -10.
These numbers are -5 and -5:
[tex]-5-5 = -10\\-5 * -5 = 25[/tex]
Then, the factorization is given by:
[tex](x-5) (x-5)\\(x-5) ^ 2 [/tex]
Answer:
[tex](x-5) ^ 2 [/tex]
michelle wants to listen to 5 compact discs. two compact discs are each 5l minutes long and the other three compact discs are each 46 minutes long. how many hours and minutes will it take michelle to listen to all 5 compact discs?
Answer:
[tex]4\ hours[/tex]
Step-by-step explanation:
we know that
1 hour=60 minutes
we know that
To find out how many hours and minutes it will take Michelle to listen to the 5 CDs, add the times for each CD.
so
[tex]2(51)+3(46)=240\ minutes[/tex]
Convert to hours
[tex]240=240/60=4\ hours[/tex]
Find the sample standard deviation and the population standard deviation of the data set.
52, 19, 44, 49, 37, 46, 52, 36, 54, 13, 14, 17, 34, 16, 51
5 - 1572
- 1519
S - 15.19
- 15.72
Answer:
See below in bold.
Step-by-step explanation:
52, 19, 44, 49, 37, 46, 52, 36, 54, 13, 14, 17, 34, 16, 51
The mean = 35.6
The absolute differences from the mean =
16.4, 16.6, 8.4, 13.4, 1.4, 10.4, 16.4, 0.4, 18.4, 22.6, 21.6, 18.6, 1.6, 19.6, 15.4
The squares of these differences =
268.96, 275.56, 70.56, 179.56, 1.96, 108.16, 268.96, 0.16, 338.56, 510.76, 466.56, 345.96, 2.56, 384.16, 237.16.
The Sum of these squares = 3459.6
Sample Variance 3459.6 / 14 = 247.11 and
Population Variance = 3459.6 / 15 = 230.64
Sample standard deviation = √247.11 = 15.72
Population Standard deviation = √230.64 = 15.19.
Sample standard deviation = √247.11 = 15.72
Population Standard deviation = √230.64 = 15.19.
What is standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
Given
52, 19, 44, 49, 37, 46, 52, 36, 54, 13, 14, 17, 34, 16, 51
The mean = 35.6
The absolute differences from the mean =
16.4, 16.6, 8.4, 13.4, 1.4, 10.4, 16.4, 0.4, 18.4, 22.6, 21.6, 18.6, 1.6, 19.6, 15.4
The squares of these differences =
268.96, 275.56, 70.56, 179.56, 1.96, 108.16, 268.96, 0.16, 338.56, 510.76, 466.56, 345.96, 2.56, 384.16, 237.16.
The Sum of these squares = 3459.6
Sample Variance 3459.6 / 14 = 247.11 and
Population Variance = 3459.6 / 15 = 230.64
Sample standard deviation = √247.11 = 15.72
Population Standard deviation = √230.64 = 15.19.
To know more about standard deviation refer to :
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I need help breaking this down
Answer:
see explanation
Step-by-step explanation:
Given
2cosΘ - [tex]\sqrt{2}[/tex] = 0 ( add [tex]\sqrt{2}[/tex] to both sides )
2cosΘ = [tex]\sqrt{2}[/tex] ( divide both sides by 2 )
cosΘ = [tex]\frac{\sqrt{2} }{2}[/tex]
Since cosΘ > 0 then Θ is in first and fourth quadrants, hence
Θ = [tex]cos^{-1}[/tex] ( [tex]\frac{\sqrt{2} }{2}[/tex] ) = [tex]\frac{\pi }{4}[/tex]
OR
Θ = 2π - [tex]\frac{\pi }{4}[/tex] = [tex]\frac{7\pi }{4}[/tex]
solutions are Θ = [tex]\frac{\pi }{4}[/tex], [tex]\frac{7\pi }{4}[/tex]
Answer:
π/4, 7π/4.
Step-by-step explanation:
2 cos O - √2 = 0
2 cos O = √2
cos O = √2/2
This is an angle in 45-45-90 triangle where the sides are in the ratio
1:1:√2 where the cosine of 45 degrees = 1 /√2 = √2/2.
In radians it is π/4.
The cosine is also positive in the fourth quadrant so the other solution is
7π/4.
What is the best first step in solving -4x + 2/5 > 5/10
A.) Add 2/5 to both sides.
B.) Subtract 2/5 from both sides.
C.) Multiply both sides by -4 and reverse the inequality symbol.
D.) Divide both sides by 10 and reverse the inequality symbol.
will mark you brainliest pls help
Answer:
B
Step-by-step explanation:
if we add (or subtract) the same amount from both sides, it does not affect the inequality and we can solve it
Answer:
b on edge 2020
Step-by-step explanation:
To rationalize the denominator of 2sqrt10/3sqrt11
Answer:
√11/√11
Step-by-step explanation:
in order to rationalize the denominator we must multiply it with the a radical that simplifies the radical in denominator
in given case radical in denominator is√11, in order to simplify it we need to multiply numerator and denominator by √11.
2√10/3√11 x √11/√11
=2√110/3(11)
=2√110/33!
For this case we must rationalize the denominator of the following expression:
[tex]\frac {2 \sqrt {10}} {3 \sqrt {11}} =[/tex]
To rationalize the denominator, that is, remove the root of the denominator, we must multiply by:
[tex]\frac {\sqrt {11}} {\sqrt {11}}[/tex]
So, we have:
[tex]\frac {2 \sqrt {10}} {3 \sqrt {11}} * \frac {\sqrt {11}} {\sqrt {11}} =\\\frac {2 \sqrt {10} * \sqrt {11}} {3 (\sqrt {11}) ^ 2} =\\\frac {2 \sqrt {110}} {3 * 11} =\\\frac {2 \sqrt {110}} {33}[/tex]
Answer:
Option B
In the figure, Triangle BAT is congruent Triangle CAT. Which statement is true by CPCTC?
CPCTC = corresponding parts of congruent triangles are congruent
BA and CA are corresponding sides for both triangles, namely twins, BA ≅ CA.
Answer: [tex]\overline{BA}\cong\overline{CA}[/tex]
Step-by-step explanation:
Given : [tex]\triangle {BAT}\cong\triangle{CAT}[/tex]
The CPCTC property of congruent triangles says that the corresponding parts of congruent triangles are congruent.
Therefore, the the corresponding angles and sides of [tex]\triangle {BAT}\text{ and }\triangle{CAT}[/tex] are congruent.
i.e. [tex]\angle {BAT}\cong\angle{CAT}[/tex]
[tex]\angle {ATB\cong\angle{ATC}\\\\\[/tex]
[tex]\angle {TBA}\cong\angle{TCA}[/tex]
and
[tex]\overline{BA}\cong\overline{CA}\\\\\overline{AT}\cong\overline{AT}\\\\\overline{TB}\cong\overline{TC}[/tex]
So, from all the options [tex]\overline{BA}\cong\overline{CA}[/tex] is the true option.
The amount of energy a microwave oven uses (in the form of electricity) is given by the function f(x)=5x+9, where x is the amount of time the microwave is turned on. The amount of energy the microwave puts out is modeled by the function g(x)=−x^2+3x+1, where x is the amount of time the microwave is turned on.
What is the difference between the amount of energy the microwave uses and the amount it puts out?
(x)=x^2+2x+8
f(x)=−x^2−2x−8
f(x)=−x^2+8x+10
f(x)=x^2−8x−10
Answer:
The difference between the amount of energy the microwave uses and the amount it puts out is x² + 2x + 8 ⇒ first answer
Step-by-step explanation:
* Lets explain how to solve the problem
- The amount of energy a microwave oven uses is given by the
function f(x) = 5x + 9
- The amount of energy the microwave puts out is given by the
function g(x) = − x² + 3x + 1
- x is the amount of time the microwave is turned on in
both functions
- To find the difference between the amount of energy the
microwave uses and the amount it puts out we will subtract
g(x) from f(x)
* Lets do that
∵ f(x) = 5x + 9
∵ g(x) = - x² + 3x + 1
∴ The difference = 5x + 9 - (-x² + 3x + 1) ⇒ multiply the bracket by (-)
- Remember that (-)(-) = (+) and (-)(+) = (-)
∴ The difference = 5x + 9 + x² - 3x - 1 ⇒ Add the like terms
∴ The difference = x² + (5x - 3x) + (9 - 1)
∴ The difference = x² + 2x + 8
* The difference between the amount of energy the microwave uses
and the amount it puts out is x² + 2x + 8
To find the difference between the energy a microwave uses and the energy it puts out, subtract the output function from the input function using the given equations. The correct answer is [tex]f(x) - g(x) = x^2 + 2x + 8[/tex] that is option A is correct.
The difference between the amount of energy the microwave uses and the amount it puts out can be calculated by subtracting the output function from the input function.
Given:
f(x) = 5x + 9 (energy used by the microwave)
[tex]g(x) = -x^2 + 3x + 1[/tex](energy output by the microwave)
Calculating the difference:
Substitute the values:
[tex]f(x) - g(x) = (5x + 9) - (-x^2 + 3x + 1)[/tex]
Simplify the expression:
[tex]f(x) - g(x) = x^2 + 2x + 8[/tex]
The coordinates of the preimage are: A(8,8) B(10,6) C(2,2) We want to reflect over y=−1 first. Our new coordinates are: A′(8, ) B′(10, ) C′(2, ) Now we will reflect over y=−7 and our new coordinates will be: A′′(8, ) B′′(10, ) C′′(2, ) We can also see that −7−(−1)=−6. We know that two reflections is the same as a translation of 2h units. So 2(−6) is a translation of −12 units down.
Answer:
1)A'(8,-10), B'(10,-8), C'(2,-4)
2)A''(8,-4), B''(10,-6), C''(2,-10)
Step-by-step explanation:
Given:
Points A(8,8) B(10,6) C(2,2)
reflection over y=-1
Perpendicular distance between points y-coordinates of points (A, B and C) and y=-1 are 9,7 and 3
after reflections, the perpendicular distance will be 18,14,6 and the points will be at
A'(8,-10), B'(10,-8), C'(2,-4)
Now
Points A(8,-10), B(10,-8), C(2,-4)
reflection over y=−7
Perpendicular distance between points y-coordinates of points (A, B and C) and y=-7 are 3,1 and 3
after reflections, the perpendicular distance will be 6,2,6 and the points will be at
A''(8,-4), B''(10,-6), C''(2,-10) !
the speed thing above the chart, Ya pretend that is not there
For this case we have:
a)
[tex]\frac {1} {10}[/tex]to convert as a percentage we have:
[tex]\frac {1} {10}[/tex] * 100% = 10%
b)
[tex]\frac {1} {4}[/tex], if we multiply the numerator and denominator by 25 we have:
[tex]\frac {25} {100}[/tex]
c)
Now we must write a fraction that represents 50%.
We have[tex]\frac {1} {2}[/tex]. If we multiply the numerator and denominator by 50 we have:
[tex]\frac {50} {100}[/tex]
Answer:
10%
[tex]\frac {25} {100}\\\frac {1} {2}[/tex]
Answer:
[tex]a=10\%\\\\b=\frac{25}{100}\\\\c=\frac{1}{2}[/tex]
Step-by-step explanation:
To find "a" you can multiply [tex]\frac{10}{100}[/tex] by 100, then this is:
[tex]a=\frac{10}{100}*100\\\\a=10\%[/tex]
To find "b", you can multiply the numerator and the denominator of the fraction [tex]\frac{1}{4}[/tex] by 25, getting:
[tex]b=\frac{1*25}{4*25}\\\\b=\frac{25}{100}[/tex]
To find "c", you can reduce the fraction [tex]\frac{50}{100}[/tex]. Then you get that this is:
[tex]c=\frac{50}{100}\\\\c=\frac{25}{50}\\\\c=\frac{5}{10}\\\\c=\frac{1}{2}[/tex]
Two statements are missing reasons. What reasons can be used to justify both statements 2 and 3 ?
Answer:
See explanation
Step-by-step explanation:
The given circle has center O.
A, B,C, and D are points on the circumference of the circle.
We want to prove that: [tex]\angle A\cong \angle D[/tex]
We need to join to B and C as shown in the attachment.
Recall that angle subtended by arc BC at the center is twice the angle subtended at the circumference by the same arc.
This implies that:
[tex] \angle O=2\angle A...(1)[/tex]
[tex]\angle O=2\angle D...(2)[/tex]
The LHS of equation (1) and (2) are equal. Therefore the RHS are also equal.
This implies that:
[tex]2\angle A=2\angle D[/tex]
[tex]\therefore \angle A\cong \angle D[/tex]
Answer:
Inscribed angles theorem
Step-by-step explanation:
Just took test on edg2020
I Need Help Answer Plz!!!
Answer:
10 inches
Step-by-step explanation:
All the sides are the same.
A summer camp cookout is planned for the campers and their families. There is room for 200 people. Each adult costs $4, and each camper costs $3. There is a maximum budget of $750. Write the system of inequalities to represent this real-world scenario, where x is the number of adults and y is the number of campers.
A.
[tex]x + y \leqslant 200 \\ 4x + 3y \leqslant 750[/tex]
B.
[tex]x + y \leqslant 750 \\ 4x + 3y \leqslant 200[/tex]
C.
[tex]x + y \leqslant 200 \\ 3x + 4y \leqslant 750[/tex]
D.
[tex] x + y \leqslant 750 \\ 3x + 4y \leqslant 200[/tex]
Answer:
[tex]A.\\\\x+y\leq200\\\\4x+3y\leq750[/tex]
Step-by-step explanation:
x - number of adults
y - number of campers
The room for 200 people: x + y ≤ 200
Each adult costs $4, and each camper costs $3: 4x and 3y
A maximum budget of $750: 4x + 3y ≤ 750
The correct option for the given scenario is option A, which includes two inequalities: one for the capacity constraint (x + y ≤ 200) and one for the budget constraint (4x + 3y ≤ 750), where x is the number of adults and y is the number of campers.
The correct system of inequalities to represent the scenario where x is the number of adults and y is the number of campers, with a room capacity for 200 people and a maximum budget of $750, is:
x+y≤2004x+3y≤750This corresponds to option A, where the first inequality represents the capacity constraint and the second inequality represents the budget constraint.
Can someone please solve this I got 7 but my teacher said its 17.
3(2x+4)=7(x-1)+2
Answer:
x=17
Step-by-step explanation:
3(2x+4)=7(x-1)+2
Simplify
6x+12=7x-7+2
6x+12=7x-5
-12 -12
6x=7x-17
Must isolate x on 1 side
-7x -7x
-x=-17
/-1 /-1
x=17
Hope this helps
Question 8 (1 point)
A population of beetles are growing according to a linear growth model. The initial population
(week 0) is Po=10, and the population after 5 weeks is P5=460.
Find an explicit formula for the beetle population after n weeks.
Pn=10+_ __*n
Answer:
[tex]P_n=10+90n[/tex]
Step-by-step explanation:
So it said it was linear and gave us two points on that line: (0,10) and (5,460).
y=mx+b is slope-intercept form where b is the y-intercept or the initial amount of beetles and m is the slope (or rate of change in population to number weeks) of the line. Our variables (x,y) are really (n,P) here.
The slope of the line can be computed using [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] where [tex](x_1,y_1) \text{ and } (x_2,y_2) \text{ are points on the line }[/tex].
You can also just line up the points vertically and subtract, then put 2nd difference over first difference.
Like this:
(5 , 460)
-(0 , 10)
--------------
5 450
So the slope is 450/5=90.
The y-intercept is where the line crosses the y-axis. A graph crosses the y-axis when it's x value is 0. Luckily, they give us the y-intercept which is (0,10) so b=10. Your problem gave us this as well and was just asking for the slope of the line.
Anyways the equation is
y=90x+10
or
y=10+90x
or since we are using P and n:
[tex]P_n=10+90n[/tex]
The explicit formula for the beetle population after n weeks is Pn = 10 + 90n.
Explanation:To find an explicit formula for the beetle population after n weeks, we need to determine the rate of growth. From the given information, we know that the population increased by 460-10=450 beetles in 5 weeks. Therefore, the rate of growth is 450/5=90 beetles per week.
To find the explicit formula, we can use the formula for a linear growth model: Pn = Po + r*n, where Pn is the population after n weeks, Po is the initial population, r is the rate of growth, and n is the number of weeks.
Substituting the given values, we have: Pn = 10 + 90n.
Learn more about Linear growth model here:https://brainly.com/question/29441614
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is c^5 - 49 a difference of squares?
a. yes
b. no
No. Since we cannot factor,
[tex]c^5-49[/tex].
Hope this helps.
r3t40
The correct answer is: b. no [tex]c^5 - 49[/tex] is not a difference of squares
Difference of squares refers to an expression of the form [tex]a^2 - b^2[/tex], which can be factored into [tex](a - b)(a + b)[/tex].
In this case, [tex]c^5 - 49[/tex] cannot be expressed in the form of [tex]a^2 - b^2[/tex] because [tex]c^5[/tex] is not a perfect square (a number raised to the power of 2) since it is c raised to the power of 5. To be a difference of squares, both terms must be perfect squares.
49 on the other is a perfect square of 7 but because of [tex]c^5[/tex] the expression [tex]c^5 - 49[/tex] cannot be converted to the form of [tex]a^2 - b^2[/tex] and is thus not considered a difference of squares.
Thus, The correct answer is: b. no [tex]c^5 - 49[/tex] is not a difference of squares
Lucy earns $5.50 per hour at a local restaurant. She earns time and a half for each hour she works on a holiday. Lucy worked sevenseven hours each day for five five days, then worked for four hours on a holiday. How much did she earn for that week?
Lucy earned a total of $225.50 for the week by combining her regular and holiday earnings.
Lucy's earnings for the week:
Regular earnings: 7 hours/day * 5 days * $5.50/hour = $192.50Holiday earnings: 4 hours * $5.50/hour * 1.5 = $33.00Total earnings for the week: $192.50 + $33.00 = $225.50Emma is 7.8 years old she is 1.2 times older than Gavin how old is Gavin
What expression is equivalent to the expression below ?m+3/m^2-16/m^2-9/m+4
Answer:
[tex]\large\boxed{\dfrac{1}{(m-4)(m-3)}=\dfrac{1}{m^2-7m+12}}[/tex]
Step-by-step explanation:
[tex]\dfrac{\frac{m+3}{m^2-16}}{\frac{m^2-9}{m+4}}=\dfrac{m+3}{m^2-16}\cdot\dfrac{m+4}{m^2-9}=(*)\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\m^2-16=m^2=4^2=(m-4)(m+4)\\m^2-9=m^2-3^2=(m-3)(m+3)\\\\(*)=\dfrac{m+3}{(m-4)(m+4)}\cdot\dfrac{m+4}{(m-3)(m+3)}\\\\\text{cancel}\ (m+3)\ \text{and}\ (m+4)\\\\=\dfrac{1}{m-4}\cdot\dfrac{1}{m-3}=\dfrac{1}{(m-4)(m-3)}\\\\\text{use\ FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=\dfrac{1}{(m)(m)+(m)(-3)+(-4)(m)+(-4)(-3)}\\\\=\dfrac{1}{m^2-3m-4m+12}=\dfrac{1}{m^2-7m+12}[/tex]
What is the Prime factorization of 1323
Answer:3, 9, 27, 7, 189
Step-by-step explanation:
The prime factorization of 1323 involves breaking it down into prime factors that multiply together to give the original number, starting with the smallest prime.
Explanation:The prime factorization of 1323 is the process of breaking down the number into its prime factors, which are numbers that are prime and multiply together to give the original number, 1323. To find the prime factors, we start by dividing the number by the smallest prime number, which is 2. Since 1323 is odd, we move to the next prime number, which is 3. We find that 1323 is divisible by 3, so we can write 1323 as 3 × 441. We continue to take 441 and factor it further, eventually finding the complete prime factorization.
A pharmacist found at the end of the day she had 5/4 as many prescriptions for antibiotics then tranquilizers. She had 18 prescriptions all together. How many did she have for tranquilizers?
Answer:
16. 5/3
Step-by-step explanation:
let the no of tranquilizer be x
therefore
5/4 + x =18
x= 18-5/4
= 16 5/3
Two-thirds of the children in the fourth - grade class are girls. If there are 18 girls, what is the total number of children in the class?
For this case, the first thing to do is define a variable.
We have then:
x: total number of childrenThen we write the equation that models the problem:
[tex]\frac {2} {3} x = 18[/tex]
From here, we clear the value of x.
We have then:
[tex]x = \frac {3} {2} (18)\\x = 3 * 9\\x = 27[/tex]
Answer:
the total number of children in the class is:
[tex]x = 27[/tex]
To calculate the total number of children in the fourth-grade class, divide the number of girls by 2 to find one-third of the class, then multiply by 3. The total class size is 27 children.
To find the total number of children in the fourth-grade class, we start by understanding that two-thirds of the children are girls. If there are 18 girls, which is two-thirds of the class, we need to calculate the full class size which constitutes three-thirds (or the whole).
Step 1: Represent two-thirds of the class as 2/3.
Step 2: Equate two-thirds of the class to the number of girls: 2/3 of the class = 18 girls.
Step 3: Find one-third of the class by dividing the number of girls by 2: 18 girls \/ 2 = 9 children.
Step 4: Calculate the full class size (which is three-thirds) by multiplying one-third of the class by 3: 9 children x 3 = 27 children.
Therefore, the total number of children in the fourth-grade class is 27.
Plz helpppp:Tammy conducted a survey to find the favorite subject of the students at her school. She asked 25 students from her math class what their favorite subje
is. Tammy concludes that math is the favorite subject of the students at her school because 60% of the students in her class like math.
Use at least two sentences to explain why Tammy's sample may not be valid. Make sure to use facts to support your answer.
Answer: Tammy's sample may not be vaild because she surveyed the students only from her class and it is likely that other classes might not like the subject maths. She might get the accurate results by surveying a larger number of people in the school instead of just her class.
Short sleeve t-shirts cost $10 and long sleeve t-shirts cost $15. If the t-shirt shop made $485 selling 38 total t-shirts, how many of each type of shirt did they sell?
Answer:
The t-shirt shop sold 21 long sleeve shirts and 17 short sleeve shirts.
Step-by-step explanation:
To solve this problem, we should create a system of equations. Let's let short sleeve t-shirts be represented by the variable s and long sleeve t-shirts be represented by the variable l.
We know that the shop sold 38 total shirts, or in other words, the amount of long sleeve and short sleeve shirts combined is 38. If we write this as an equation, we get: s + l = 38.
We can make another equation with the prices of the shirts. If we take each type of shirt and multiply each price by the number sold and add them together, we should get the shop's total profits. Represented as an equation, this is: 10s + 15l = 485.
Now that we have two equations, we should try to solve the system. In this case, it is easiest to use substitution, so we are going to rewrite the first equation in terms of one variable.
s + l = 38
s = 38 - l
If we substitute this equivalent value for the variable s into the second equation, we get:
10s + 15l = 485
10(38 - l) + 15l = 485
Now we have an equation that only has one variable, so we can simplify both sides and then isolate the variable.
380 - 10l + 15l = 485
380 + 5l = 485
5l = 105
l = 21
Now, we can substitute this value for l back into the first equation to solve for the variable s.
s + l = 38
s + 21 = 38
s = 17
Therefore, the t-shirt shop sold 21 long sleeve shirts and 17 short sleeve shirts.
Hope this helps!
Which linear function represents the line given by the point-slope equation y + 7 = –2/3(x + 6)? Here are the options f(x) = –2/3x – 11, f(x) = –2/3x – 1, f(x) = –2/3 + 3, f(x) = –2/3x + 13.
Answer:
The correct answer is: f(x) = –2/3x – 11
Step-by-step explanation:
We have to convert the line given in point slope form to a form which can be compared by the given options
So,
y+7=-2/3(x+6)
[tex]y=-\frac{2}{3}(x+6)\\ y+7=-\frac{2}{3}x+(6)(-\frac{2}{3}) \\ y+7=-\frac{2}{3}x-4\\y=-\frac{2}{3}x-4-7\\y=-\frac{2}{3}x-11[/tex]
Therefore the correct answer is: f(x) = –2/3x –11 ..
Your parents gave you a gift card for your favorite coffee shop. The card was worth $50
when you got it. Each day, you buy a drink for $3. Which equation shows the value on
the gift card over time?
Final answer:
The equation that shows the value on the gift card over time is: Value on gift card = Initial value - Total amount spent.
Explanation:
The equation that shows the value on the gift card over time is: Value on gift card = Initial value - Total amount spent.
Since the initial value of the gift card is $50 and each day a drink costs $3, the equation can be written as: Value on gift card = 50 - 3x, where x represents the number of days.
This equation will give you the value remaining on the gift card after x days of buying a $3 drink.
What is the LCD of 5/6 and 2/5 ?
Answer:
30
Step-by-step explanation:
Find lowest common multiple of 5 and 6
Multiples of 5 Multiples of 6
5 × 1 = 5 6 × 1 = 6
5 × 2 = 10 6 × 2 = 12
5 × 3 = 15 6 × 3 = 18
5 × 4 = 20 6 × 4 = 24
5 × 5 = 25 6 × 5 = 30
5 × 6 = 30
5 × 7 = 35
5 × 2 = 10
5 × 3 = 15
5 × 4 = 20
5 × 5 = 25
5 × 6 = 30
5 × 7 = 35
30 is the lowest number which comes in both lists
It's 30... if your looking at a simple answer, it's 30.
Find the equation of the line.
Use exact numbers.
Y =
A truck with 36-in.-diameter wheels is traveling at 55 mi/h.
Find the angular speed of the wheels in rad/min
Answer:
The angular speed is 3,227 rad/min
Step-by-step explanation:
Remember that
1 mile=63,360 inches
step 1
Find the circumference of the wheels
The circumference is equal to
[tex]C=\pi D[/tex]
we have
[tex]D=36\ in[/tex]
substitute
[tex]C=\pi (36)[/tex]
[tex]C=36\pi\ in[/tex]
step 2
we know that
The speed of the wheel is 55 mi/h
Convert to mi/min
55 mi/h=55/60 mi/min
Convert to in/min
(55/60) mi/min=55*63,360/60 in/min= 58,080 in/min
we know that
The circumference of the wheel subtends a central angle of 2π radians
so
using proportion
Find out how much radians are 58,080 inches
[tex]\frac{36\pi }{2\pi }=\frac{58,080}{x} \\\\x=2*58,080/36\\\\x=3,226.67 \ rad[/tex]
therefore
The angular speed is 3,227 rad/min
Final answer:
To calculate the angular speed in radians per minute for a truck with 36-inch diameter wheels traveling at 55 mi/h, convert the diameter to radius in meters, convert the speed to meters per minute, and then use the relationship v = r theta.
Explanation:
To find the angular speed of the wheels in radians per minute, we can use the relationship between linear speed and angular speed, which is given by v = r * theta, where v is the linear speed, r is the radius of the wheel, and theta is the angular speed.
First, convert the diameter to radius: radius = diameter / 2 = 36 in / 2 = 18 in. Then, convert inches to meters as 1 inch is 0.0254 meters. So, radius in meters = 18 in * 0.0254 m/in = 0.4572 m.
Next, convert the speed from miles per hour to meters per minute:
Convert miles to meters: 1 mile = 1609.34 meters,
Speed in meters per minute: 55 mi/h * 1609.34 m/mi * 1h/60min = 1,486.86 m/min.
Now we can find the angular speed: theta = v / r = 1,486.86 m/min / 0.4572 m = 3,252.3 rad/min.