Answer:
The data set "types of fruit at the grocery store" is qualitative.
The correct answer is B.
The correct option is a. quantitative, discrete.
The data set "types of fruit at the grocery store" is quantitative because it involves counting the number of different types of fruit, which is a numerical value. Furthermore, it is discrete because the count of fruit types will result in whole numbers, with no fractional or continuous values between them. For example, one cannot have 3.5 types of fruit; it must be a whole number such as 3 or 4. Therefore, the data is not qualitative as it is not about the characteristics or attributes of the fruit but rather the count of different categories of fruit. It is also not continuous as the number of fruit types cannot vary smoothly and must be counted in whole units.
You downloaded a video game to your computer. You have a 60-minute free trial of the game. It takes 5 1/6 minutes to set up the game and 7 1/3 minutes to play each level. You want to find out how many levels you can play for free. Which inequality describes the number of levels, ł, you can play in 60 minutes? Choose 1 answer: A. 5 1/6 + (7 1/3) ł >_ 60 B. 5 1/6 + (7 1/3) ł <_ 60 C. (7 1/3) ł - 5 1/6 >_ 60 D. (7 1/3) ł - 5 1/6 <_ 60 ( the _ goes under the < or > cause I can’t do it on my phone) Can you play 6 levels during your free trial? Choose 1 answer: yes or no
Answer:
Question 1: b Question 2: yes
Step-by-step explanation:
The variable must go with 7+1/3 calculate time for all the levels. Then add 5+1/6. It must be less than or equal to because you want to play all 6 levels. You can play all 6 when you plug in 6 as the variable. It is less than 60
Classify the system of equations
- 1/2x = -6 - y
3+y= 1/2x + 4
(2 points, 1 for work shown, 1 for correct classification with reasoning)
Answer: Inconsistent.
Step-by-step explanation:
The equation of the line in Slope-intercept form is:
[tex]y=mx+b[/tex]
Where m is the slope and b is the y-intercept.
Solve for y from each equation:
Equation 1:
[tex]-\frac{1}{2} x = -6 - y\\\\y-\frac{1}{2} x = -6\\\\y=\frac{1}{2} x-6[/tex]
Equation 2:
[tex]3+y= \frac{1}{2} x + 4\\\\y= \frac{1}{2} x + 4-3\\\\y= \frac{1}{2} x+1[/tex]
A system of equations can be classified by its number of solutions.
You can observe that the slopes of both equations are the same but the y-intercepts are different, then these lines are parallel, which means that they do not intersect.
By definition, when to lines are parallel there is NO SOLUTION and the system is classified as "Inconsistent".
You borrow $4000 from the bank at 3% annual interest compounded monthly. The monthly payment is $200. What is the balance after the third payment?
The balance of a $4000 loan at a 3% annual interest rate compounded monthly after three payments of $200 each is $3428.58.
To find the balance after the third payment of a $4000 loan, compounded monthly at an annual interest rate of 3%, we must first determine the monthly interest rate. The annual rate of 3% means a monthly rate of 0.25% (3%/12 months). Next, we'll apply the loan payment process three times to calculate the remaining balance.
Month 1: Initial balance is $4000. Interest for the month is $4000 * 0.0025 = $10. The balance before payment is $4010. After a $200 payment, the new balance is $4010 - $200 = $3810.Month 2: Interest for the month is $3810 * 0.0025 = $9.53. The balance before payment is $3810 + $9.53 = $3819.53. After a $200 payment, the new balance is $3819.53 - $200 = $3619.53.Month 3: Interest for the month is $3619.53 * 0.0025 = $9.05. The balance before payment is $3619.53 + $9.05 = $3628.58. After the third $200 payment, the new balance is $3628.58 - $200 = $3428.58.The balance after the third payment is $3428.58.
which statement best describes the association between variables X and variable Y?
*moderate positive association
*moderate negative association
*perfect negative association
*perfect positive association
someone please help me
Answer:
moderate negative
Step-by-step explanation:
a perfect would be a rate, I believe.
The statement which best describes the association between variables X and variable Y is:
moderate negative association
Step-by-step explanation:Since by looking at the scatter plot we see that the Y-value is decreasing with the increasing x-value i.e. the two variables are in inverse proportion.
Hence, the two variables has a negative association.
Also, when we will draw a line of best fit we will observe that not all the data points will lie on the trend line but they will be closely related to the line of best fit.
Hence, the relationship is moderate.
Hence the answer is:
Moderate negative association.
4/3+6=1/4x
Solve the equation
Answer:
Step-by-step explanation:
cross multiply
4*4x=1*3+6
16x=9
x=9/16
5(x + 2)
F(x) -
y - 11x + 7)
Answer:
Problem:
Solve x+y=7;x+2y=11
Steps:
I will try to solve your system of equations.
x+y=7;x+2y=11
Step: Solvex+y=7for x:
x+y+−y=7+−y(Add -y to both sides)
x=−y+7
Step: Substitute−y+7forxinx+2y=11:
x+2y=11
−y+7+2y=11
y+7=11(Simplify both sides of the equation)
y+7+−7=11+−7(Add -7 to both sides)
y=4
Step: Substitute4foryinx=−y+7:
x=−y+7
x=−4+7
x=3(Simplify both sides of the equation)
Answer:
x=3 and y=4
Brett is paid $18.95 per hour with time and a half for overtime. What will his gross pay be for a pay period in which he worked 42 hours one week and 36 hours the next week for a total of 78 hours?
The gross pay will be $1496.78
What is Unitary Method ?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Brett is paid $18.95 per hour.
For 0 to 40 hours a week,
For any hours over 40, Brett makes
= 1.5 ($18.95)
= $28.425/hour
In Week 1: 40 hours x $18.95/hour = $758
2 hours x $28.425/hour = 56.85
Week 2: 36 hours x $18.95/hour = 682.2
So, total pay= 758 + 56.58+ 682.2 = $1496.78
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Final answer:
Brett's gross pay for working 42 hours one week and 36 hours the next, for a total of 78 hours, is $1495.05, which includes 2 hours of overtime pay.
Explanation:
Brett is paid an hourly wage of $18.95, with overtime paid at 1.5 times his regular rate. To calculate Brett's gross pay for the two-week pay period where he worked 42 hours one week and 36 hours the next week, we have to account for the fact that he worked 2 hours of overtime in the first week (since he worked more than 40 hours).
Step-by-Step Calculation
Regular hours for two weeks: 40 hours + 36 hours = 76 hours.Overtime hours for the first week: 42 hours - 40 hours = 2 hours.Calculate regular pay: 76 hours x $18.95/hour = $1438.20.Calculate overtime pay: 2 hours x ($18.95/hour x 1.5) = $56.85.Add regular and overtime pay: $1438.20 + $56.85 = $1495.05.Brett's gross pay for the 78 hours worked would be $1495.05.
Let f(x) =Sqrt 9x and g(x) =x+7 whats the smallest number that's in the domain of f ° g
The smallest number that's in the domain of f ° g is x = 0.
Explanation:The function f(x) = √(9x) represents the square root of 9x.
The function g(x) = x + 7 represents adding 7 to x. To find the smallest number that is in the domain of f ° g, we need to determine the values of x that satisfy both f(x) and g(x).
We can start by looking at the domain of g(x), which includes all real numbers. So any value of x will work for g(x).
Next, we need to consider the domain of f(x). Since taking the square root of a negative number is not defined in the real number system, we must ensure that 9x is positive or zero.
So we set 9x ≥ 0 and solve for x: x ≥ 0. This means any non-negative value of x will work for f(x).
Now, to find the smallest number in the domain of f ° g, we need to find the intersection of the domains of f(x) and g(x).
Since any value of x will work for g(x) and only non-negative values of x will work for f(x), the smallest number that satisfies both functions is x = 0.
15 points!!!
Two right triangles are shown below.
Which statement is true?
There is a dilation centered at the origin with scale factor 2 transforming triangle I into triangle III.
There is a dilation centered at (-2,0) with scale factor 2 transforming triangle I into triangle III.
There is a dilation centered at a point off of the x-axis transforming triangle I into triangle III.
There is no dilation transforming triangle I into triangle III.
Answer:
The correct option is 4.
Step-by-step explanation:
If a figure it dilated by scale factor k, then the image and preimage are similar figures and their corresponding sides are proportional.
In triangle I, the base of the triangle is 1 unit and length of the perpendicular is 1 units.
In triangle II, the base of the triangle is 1 unit and length of the perpendicular is 2 units.
[tex]\frac{1}{1}\neq \frac{1}{2}[/tex]
The corresponding sides are not proportional. It means both triangles are not similar. So, there is no dilation transforming triangle I into triangle II.
Therefore the correct option is 4.
Answer:
There is no dilation transforming triangle I into triangle II.
Step-by-step explanation:
2 qt/min= how many gal/s
The flow rate is 2 quarts per minute. There are 4 quarts in a US gallon, so 2 quarts divide 4 quarts per US gallon = 0.5 gallons per minute There are 60 seconds in a minute, so the flow rate is 0.5 gallons per minute divide 60 seconds per minute = 0.0083 gallons per second
Converting 2 quarts per minute to gallons per second requires the use of two conversion factors. First, quarts are converted to gallons by dividing by 4. Then, minutes are converted to seconds by dividing by 60. After performing these steps, it is found that 2 quarts per minute is approximately equal to 0.00833 gallons per second.
Explanation:The student is asking to convert a flow rate from quarts per minute to gallons per second. There are a few fundamental conversions you need to use to find the answer. Firstly, remember that 1 gallon (gal) is equivalent to 4 quarts (qt). So, to convert the quarts to gallons, divide the quarts by 4. Secondly, there are 60 seconds in a minute; thus, you have to convert the minutes to seconds by dividing by 60.
Let's go step-by-step:
Convert quarts to gallons: 2 quarts/minute ÷ 4 = 0.5 gallons/minuteConvert minutes to seconds: 0.5 gallons/minute ÷ 60 = 0.00833 gallons/secondTherefore, 2 quarts per minute is approximately equal to 0.00833 gallons per second.
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Quadrilateral JKLM is a rhombus. The diagonals intersect at N. If the measure of angle KJL is 2x + 5° and angle MJN = 3x – 8 find the measure of angle KLM.
Answer:
The measure of angle KLM is 62°
Step-by-step explanation:
* Lets revise the properties of the rhombus
- The rhombus has 4 equal sides in length
- Every two opposite angles are equal in measure
- The two diagonals bisect each other
- The two diagonals perpendicular to each other
- The two diagonals bisect the vertices angles
* Lets solve the problem
∵ JKLM is a rhombus
∴ m∠MJK = m∠KLM ⇒ opposite angles in the rhombus
∵ JL and KM are diagonals in the rhombus and intersect each
other at N
∴ JL bisects ∠MJK
∴ m∠KJL = m∠MJN
∵ m∠KJL = (2x + 5)°
∵ m∠MJN = (3x - 8)°
∴ 2x + 5 = 3x - 8 ⇒ subtract 2x from both sides
∴ 5 = x - 8 ⇒ add 8 to both sides
∴ 13 = x
∴ The value of x = 13
∵ m∠KJL = (2x + 5)° ⇒ substitute the value of x
∴ m∠KJL = 2(13) + 5 = 26 + 5 = 31°
∵ m∠KJL = 1/2 m∠MJK
∴ m∠MJK = 2 m∠KJL
∴ m∠ MJK = 2 × 31° = 62°
∵ m∠MJK = m∠KLM ⇒ opposite angles in the rhombus
∴ m∠KLM = 62°
8s-10=27-(3s-7) What does “s” equal?
Answer:
s = 4
Step-by-step explanation:
Solve for s:
8 s - 10 = 34 - 3 s
Add 3 s to both sides:
8 s + 3 s - 10 = (3 s - 3 s) + 34
3 s - 3 s = 0:
8 s + 3 s - 10 = 34
8 s + 3 s = 11 s:
11 s - 10 = 34
Add 10 to both sides:
11 s + (10 - 10) = 10 + 34
10 - 10 = 0:
11 s = 34 + 10
34 + 10 = 44:
11 s = 44
Divide both sides of 11 s = 44 by 11:
(11 s)/11 = 44/11
11/11 = 1:
s = 44/11
The gcd of 44 and 11 is 11, so 44/11 = (11×4)/(11×1) = 11/11×4 = 4:
Answer: s = 4
Two positive integers have a sum of 10 and a product of 21. What are the integers?
Answer:
3 and 7Step-by-step explanation:
[tex]x,y-\text{positive integers}\\\\\text{The system of equations:}\\\\\left\{\begin{array}{ccc}x+y=10&\text{subtract}\ y\ \text{from both sides}\\xy=21\end{array}\right\\\\\left\{\begin{array}{ccc}x=10-y&(1)\\xy=21&(2)\end{array}\right\\\\\text{substitute (1) to (2):}\\\\(10-y)(y)=21\qquad\text{use the distributive property}\ a(b-c)=ab-ac\\\\10y-y^2=21\qquad\text{subtract 21 from both sides}\\\\-y^2+10y-21=0\qquad\text{change the signs}\\\\y^2-10y+21=0\\\\y^2-3y-7y+21=0\\\\y(y-3)-7(y-3)=0[/tex]
[tex](y-3)(y-7)=0\iff y-3=0\ \vee\ y-7=0\\\\y-3=0\qquad\text{add 3 to both sides}\\\\y=3\\\\y-7=0\qquad\text{add 7 to both sides}\\\\y=7\\\\\text{Put the value of}\ y\ \text{to (1):}\\\\x=10-3=7\ or\ x=10-7=3[/tex]
Which pay rates are common ways employers pay employees?
commission
daily pay
hourly pay
quarterly pay
salary
Reset
help ASAP
Answer:
The employers pay their employees based on hourly rates, commission and salary.
Step-by-step explanation:
The employees get their pay based on hourly rates that can range from a minimum hourly rate of say $12 per hour to any maximum figure like $40 per hour.
The final salary is based on the numbers of hours worked multiplied by the hourly rate.
Secondly, the pays are also commission based. That is your base salary plus the commission.
The salary is typical in management positions. These are not hourly based but a lump sum pay.
So, the correct answers are : commission, hourly pay and salary.
Answer:
commission
hourly pay
salary
Step-by-step explanation:
PLATO USERS
Write the fraction 72/81
in simplest form.
Answer: 8/9
Hope it helped!
Answer:
8/9
Step-by-step explanation:
Find the GCD (or HCF) of numerator and denominator
GCD of 72 and 81 is 9
72 ÷ 9
81 ÷ 9
= 8/9
Please help! Thank you!!
Answer:
BC = 11
Step-by-step explanation:
Substitute x = 5 into the expression for BC
BC = 2x + 1 = (2 × 5) + 1 = 10 + 1 = 11
11 is the answer good luck
7. The temperature in Springfield at 10:00 a.m. was 78°F. During the day, it dropped to 56°F. Write and solve an equation to
find the decrease in temperature
Answer:
The equation is equal to 78°-x=56°
The decrease in temperature is 22°
Step-by-step explanation:
Let
x-----> the decrease in temperature
we know that
The equation that represent this situation is equal to
78°-x=56°
Solve for x
x=78°-56°
x=22°
Answer:
The required equation is [tex]78^\circ F-t=56^\circ F[/tex]
The decrease in temperature is 22°F.
Step-by-step explanation:
Given : The temperature in Springfield at 10:00 a.m. was 78°F. During the day, it dropped to 56°F.
To find : Write and solve an equation to find the decrease in temperature ?
Solution :
We have given that temperature is dropped i.e. there is decrease in teh temperature.
Let the decrease in the temperature be 't'.
According to question,
The temperature in Springfield at 10:00 a.m. was 78°F. During the day, it dropped to 56°F.
i.e. the required equation is [tex]78^\circ F-t=56^\circ F[/tex]
Solve,
[tex]t=78^\circ F-56^\circ F[/tex]
[tex]t=22^\circ F[/tex]
The decrease in temperature is 22°F.
I need help on this plz
Answer:
$51200
Step-by-step explanation:
Simply do this: 2¹⁰ × 50. You are doing this because you are doubling it for each year that goes by.
I am joyous to assist you anytime.
What is the positive difference between the square of the sum of the first five positive integers and the sum of the first five positive perfect squares?
Answer:
200Step-by-step explanation:
The square of the sum of the first five positive integers:
(1 + 2 + 3 + 4 + 5)² = 15² = 225
The sum of the first positive perfect square:
1² + 2² + 3² + 4² + 5² = 1 + 4 + 9 + 16 + 25 = 55
225 - 55 = 200
The positive difference between the square of the sum of the first five positive integers and the sum of the first five positive perfect squares is 170. This is obtained by taking the sum of first five numbers, squaring the sum and subtracting the sum of first five perfect squares.
Calculate the positive difference:The sum of first five positive integers = 1+2+3+4+5 = 15
Square of the sum of the first five positive integers = 15² = 225
The sum of the first five positive perfect squares =1²+2²+3²+4²+5²
=1+4+9+16+25
=55
The positive differenece = 225-55=170
Hence the positive difference between the square of the sum of the first five positive integers and the sum of the first five positive perfect squares is 170.
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john order 3 burgers and 2 fries for $12.15. Emily bought 4 burgers and 3 fries for $16.80. How much did the pay for each burger and order of fries?
Answer:
They paid $2.85 for each burger and $1.8 for each order of fries
Step-by-step explanation:
It will be solved simultaneously,
let x represent burger and y represent fries
John's order gives the first equation
3x + 2y = 12.15 ........(1)
Emily's order gives the second equation
4x + 3y = 16.80 ..........(2)
multiply equation (1) by 3 and equation (2) by 2 so as to eliminate y
9x + 6y = 36.45 ....... (3)
8x + 6y = 33.6 ........... (4)
subtract equation (4) from (3)
9x - 8x + 6y -6y = 36.45 - 33.6
x = 2.85
substitute x= 2.85 in equation (1)
3(2.85) + 2y = 12. 15
8.55 + 2y = 12.15
2y = 12.15 -8.55
2y = 3.6
y = 1.8
Answer:
Cost of burger = $2.85 and Cost of fries = $ 1.80.
Step-by-step explanation:
Given : john order 3 burgers and 2 fries for $12.15. Emily bought 4 burgers and 3 fries for $16.80.
To find : How much did the pay for each burger and order of fries.
Solution : We have given 3 burgers and 2 fries for $12.15.
Let the cost of 1 burger = x .
Let the cost of 1 Fries = y .
3 x + 2 y = $12.15 ------(1)
4 x + 3 y = $16.80-----(2)
On multiplying (i) by 4 and (ii) by 3 and subtracting the equation .
12x + 8y = $48 .60
(-)12x +(-) 9y = (-)$50 .40
_____________
0 -y = -$ 1.80
y = $ 1.80.
3x + 2(1.80) = $12.15 .
3x + 3.60 = 12.15
3x = 12.15 - 3.60
3x = 8.55
On dividing both sides by 3.
x = $2 .85
Therefore, Cost of burger = $2.85 and Cost of fries = $ 1.80.
at a basketball game at team made 55 successful shots they were a combination of one and two point shots the team scored 92 points in all right and solve a system of equations to find out the number of each type of shot
Final answer:
To determine the number of one-point and two-point shots made by a basketball team that scored 92 points from 55 shots, set up a system of equations. Solve the system to find that the team made 18 one-point shots and 37 two-point shots.
Explanation:
Finding the Number of One-Point and Two-Point Shots
Let's define x as the number of one-point shots and y as the number of two-point shots. We then have the following system of equations based on the information provided:
x + y = 55 (Total number of successful shots)
1x + 2y = 92 (Total points scored)
To solve for x and y, we can use either substitution or elimination methods.
Using substitution:
Solve the first equation for x: x = 55 - y.
Substitute x in the second equation: 1(55 - y) + 2y = 92.Simplify and solve for y: 55 - y + 2y = 92, which simplifies to y = 37.Substitute y back into the first equation to find x: x = 55 - 37 = 18.The team made 18 one-point shots and 37 two-point shots.
Which amount is a reasonable tip for an airport skycap? A. $2 total B. $2 per bag C. $5 per bag
Answer:
Step-by-step explanation:
B or C depending on how many bags you have
A reasonable tip for an airport skycap is generally $2 per bag, reflecting both the service provided and the quantity of luggage.
The question asks about the appropriate tip amount for an airport skycap. A common guideline for tipping skycaps is $2 per bag, which is considered to be a reasonable amount. Tipping $5 per bag may be considered generous in many cases, and a flat rate of $2 in total could be seen as insufficient unless you only have one bag. The tip should reflect the quality of service provided and the number of bags. The provided information regarding airline costs and opportunity costs of time at airports is not directly related to tipping skycaps but does highlight the broader context of airport expenses and the value of time for air travelers.
I need this question
Answer:
2
Step-by-step explanation:
7 divided by 4 equals 1.75 then round to nearest tenth you get 2.
the answer is 1.8 because 1.75 is getting rounded by the 7 place which is the tenths place
Roxanne decides she's going to make cookies. Her recipe requires her to use 1 1/4 cup of sugar for each batch. Roxanne's Mom checked and they have 15 cup od sugar in the house. How many batches of cookies can Roxanne make with the sugar they have?
Answer:
i was a little unclear about your sugar amount..
Step-by-step explanation:
if the amount was 1 1/4 ( 1 cup and 1/4 cup) them the answer would be 12
12 x 1.25 = 15
if the sugar amount was just 1/4 cup of sugar the answer would be 60
.25 x 15 = 60
In the figure, mAB = 39° and mCD = 17°. The diagram is not drawn to scale.
What is the value of x?
A. 56°
B. 47.5°
C. 28°
D. 19.5°
It’s c which is 28 degree Celsius
The value of x will be equal to 28. The correct option is C.
What is intersecting chord theorem?'The intersecting chords theorem is a statement that describes a relation of the four-line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal.'
According to the given problem,
Given,
AB = 39CD = 17We know, according to intersecting chords theorem,
⇒ x = [tex]\dfrac{CD + AB}{2}[/tex]
⇒ x = [tex]\dfrac{56}{2}[/tex]
⇒ x = 28
Hence, we can conclude, that the value of x is 28.
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surface area of a pyramid. The base is a square with sides 4 inches long. the other faces are isosceles triangles. the ratio of the height of each triangle to its base is 3:2. Give the base length and the height of each triangular face
Answer:
Base of each triangular face = 4 inches
Height of each triangular face = 6 inches
Step-by-step explanation:
The length of each side of the square base is the base of each isosceles triangle forming the pyramid.
We know from our problem that the ratio of the height of each triangle to its base is 3:2, so [tex]\frac{height}{base} =\frac{3}{2}[/tex]. We also know that the base is a square with sides 4 inches long, since the bade of the square is the base of the isosceles triangle, [tex]base=4[/tex].
Replacing the value of the base in our proportion:
[tex]\frac{height}{base} =\frac{3}{2}[/tex]
[tex]\frac{height}{4} =\frac{3}{2}[/tex]
Multiply both sides by 4
[tex]\frac{height}{4}*4 =\frac{3}{2}*4[/tex]
[tex]height=\frac{3*4}{2}[/tex]
[tex]height=\frac{12}{2}[/tex]
[tex]height=6[/tex]
We can conclude that he base of each isosceles triangle is 4 inches and its height is 6 inches.
Which polynomial is in standard form?
Answer:
(C) 19x+6^2+2
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
edge 2021
What is the value of x in this figure?
143√
282√
28
283√
Answer:
Third option: 28
Step-by-step explanation:
You need to remember the following identity:
[tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]
In the right triangle shown in the figure, you can identify:
[tex]\alpha=30\°\\opposite=14\\hypotenuse=x[/tex]
Then, you need to substitute the corresponding values into [tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]:
[tex]sin(30\°)=\frac{14}{x}[/tex]
Now, you can solve for "x":
[tex]xsin(30\°)=14\\\\x=\frac{14}{sin(30\°)}\\\\x=28[/tex]
Answer:
The value of x is 28 units
Step-by-step explanation:
Given a right angled triangle with one side 14 units and one angle 30°
we have to find the value of x
By trigonometric ratios
[tex]\sin \theta=\frac{Perpendicular}{Hypotenuse}[/tex]
[tex]\sin 30^{\circ}=\frac{14}{x}[/tex]
[tex]\frac{1}{2}=\frac{14}{x}[/tex]
[tex]x=14\times 2=28 units[/tex]
Hence, the value of x is 28 units.
Option C is correct
A water trough is in the shape of a trapezoidal prism with the dimensions shown below.
A). find total volume of water that the trough can hold
Answer:
24ft^3
Step-by-step explanation:
Hope it helped you!
Answer:
24 ft.
Step-by-step explanation:
Someone please show a quicker way! (Done inefficiently in my head.)
((1.5 x1.2) + (((1.2 x .5)/2) x 2)) x 10 = 24
6. A prism has bases that are equilateral triangles with sides lengths of 10 inches and a length of 30 inches.
Determine the volume of the prism to the nearest cubic inch. Show how you arrived at your answer
30 in
10 in
ON
Answer:
The volume of the prism is [tex]1,299\ in^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the 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]L=30\ in[/tex]
Find the area of the base B
The area of a equilateral triangle is equal to
[tex]B=\frac{1}{2}(10)^{2} sin(60\°)[/tex]
[tex]B=25\sqrt{3}\ in^{2}[/tex]
substitute
[tex]V=(25\sqrt{3})(30)=1,299\ in^{3}[/tex]
The volume of the traingular prism is 1,280.85 in³.
Volume of the prismThe volume of the prism is determined using the following formulas as show below;
V = Bh
where;
B is the base area of the prismh is the height of the prismBase area is calculated as follows;
[tex]A = \frac{a^2\sqrt{3} }{4} \\\\A = \frac{10^2 \times \sqrt{3} }{4} \\\\A = 25\sqrt{3} \ in^2[/tex]
Height of the prism[tex]L^2 = (\frac{a}{2} )^2 + h^2\\\\h^2 = L^2 - (\frac{a}{2} )^2\\\\h^2 = 30^2 - (\frac{10}{2} )^2\\\\h^2 = 875\\\\h = \sqrt{875} \\\\h = 29.58 \ in[/tex]
Volume of the prismV = 25√3 x 29.58
V = 1,280.85 in³
Learn more about volume of prism here: https://brainly.com/question/23963432