Answer:
The base is 27 units long.
Step-by-step explanation:
This is a solve the system question. Call the length of the base B and the length of each leg L. We are told:
[tex]B=1.5L[/tex]
and
[tex]B+2L=63[/tex]
Sub the first equation into the second:
[tex]1.5L+2L=63\\3.5L=63\\L=18[/tex]
Now that we have the leg length, sub that into either of the original equations to find the base. I'll use the first equation:
[tex]B=1.5(18)\\B=27[/tex]
Math lovers i need your help
Part (i)
Compute the slope of the line through the two points (0,0) and (4,8)
m = (y2 - y1)/(x2 - x1)
m = (8-0)/(4-0)
m = 8/4
m = 2
The slope of this line is 2, so,
velocity = 2 m/s==============================================
Part (ii)
The two points we're working with are (4,8) and (6,8). The slope is...
m = (y2 - y1)/(x2 - x1)
m = (8-8)/(6-4)
m = 0/2
m = 0
Horizontal lines always have a slope of 0 to indicate no change in height.
The velocity is 0 m/s.==============================================
Part (iii)
Same idea as the previous parts. The endpoints are (6,8) and (9,14)
m = (y2 - y1)/(x2 - x1)
m = (14-8)/(9-6)
m = 6/3
m = 2
This piece also has slope 2. This piece is parallel to the first piece. Parallel lines have equal slopes but different y intercepts.
velocity = 2 m/s==============================================
Part (iv)
(a) The average velocity from 0 to 4 seconds is the exact same as the velocity we computed earlier in part (i). The answer is 2 m/s(b) We travel 8 meters in 6 seconds, so the average velocity is 8/6 = 4/3 = 1.33 m/s approximately. You can use the slope formula for the endpoints (0,0) and (6,8) to get the same result.(c) The average velocity is 14/9 = 1.56 m/s approximately because we travel 14 meters in 9 seconds. You can use the slope formula for the endpoints (0,0) and (9,14).As you can see, with average velocity, all we care about are the starting and ending points. We aren't concerned at all with what happens in between.
Comparing the results for part (i) and part (iv)(b), we see that the velocity has gone down. This is due to the flat portion in which you aren't moving.
Carol is solving the inequality 3
have?
There are infinitely many solutions.
There are only two solutions.
There is only one solution.
There are no solutions.
Answer:
There are infinitely many solutions
Step-by-step explanation:
Firstly, I need to change f to x as the system won’t accept the word f
Let’s take a look at the question;
3 is less than x
The domain of our answer lies in the the range of values where we have numbers that are greater than 3
This means we can rewrite our inequality as x is greater than 3
Now, simply because we have an infinite amount of numbers which are greater than 3 of which x can take any of the values, we can conclude that the number of values we have for x are infinite and does not end
This makes us have infinitely many solutions for the value of x
A rectangular prism has a length of 4.5 cm, a width of
10 cm, and a height of 2.5 cm. What is the volume of
the prism?
11.25 cm
17 cm
112.5 cm3
1,125 cm3
2.5 cm
10 cm
4.5 cm
Answer:112.5
Step-by-step explanation: multiply then all together length then width them height
Answer:
112.5
Step-by-step explanation:
i did the assignment
A circle is cut into congruent sections and arranged to form a figure that approximates a parallelogram. Find the approximate height of the figure when its area is 12.25π square centimeters.
Answer:
The height is 3.43 centimeters, approximately.Step-by-step explanation:
Notice that there are 16 pieces from the circle, which means each sector has an angle of
[tex]\theta = \frac{360\°}{16}=22.5\°[/tex]
Where all sectors have equal area.
Now, the area of the whole circle is [tex]12.25 \pi \ cm^{2}[/tex], if we use the formula of its area, we'll find the radius of the circle
[tex]A= \pi r^{2}\\ 12.25\pi = \pi r^{2}\\ r=\sqrt{12.25} \approx 3.5[/tex]
Notice that each piece works as an isosceles triangle, because each side is the radius, that is, they have the same length. So far, we know the sides of the isosceles triangle and one internal angle.
To find the height of the one piece, we need to use trigonometric reasons, because the height divides a triangle in two equal right triangles.
[tex]cos(11.25\°)=\frac{h}{3.5}\\ h=3.5 \times cos(11.25 \°)\\h \approx 3.43[/tex]
Therefore, the height is 3.43 centimeters, approximately.
A deck of playing cards has four suits, with thirteen cards in each suit consisting of the numbers 2 through 10, a jack, a queen, a king, and an ace. The four suits are hearts, diamonds, spades, and clubs. A hand of five cards will be chosen at random. Which statement is true?
Answer:
Step-by-step explanation:
Which statements are true? Check all that apply.
The total possible outcomes can be found using 52C5.
The total possible outcomes can be found using 52P5.
The probability of choosing two diamonds and three hearts is 0.089.
The probability of choosing five spades is roughly 0.05
The probability of choosing five clubs is roughly 0.0005.
Since it can be chosen in any order, we use combination and not permutation. The number of ways of choosing 5 cards from a group of 52 cards is 52C5.
The probability of choosing two diamonds and three hearts = [tex]\frac{^{13}C_2*^{13}C_3}{^{52}C_5} = 0.0086[/tex] so the third one is not true.
The probability of choosing five spades = [tex]\frac{^{13}C_5}{^{52}C_5}[/tex] ≈ 0.0005. The fourth statement is not true
The probability of choosing five clubs = [tex]\frac{^{13}C_5}{^{52}C_5}[/tex] ≈ 0.0005, the fifth one is.
So the answer is the first and fifth statement.
The probability of selecting a combination of cards is given by the ratio of
the ways of selecting the cards to the number of possible outcomes.
The true statements are;
The total number possible outcomes is ₅₂C₅.The probability of choosing five clubs is roughly 0.0005.Reasons:
First statement;
Number of cards in the deck of playing cards = 52
The number of possible outcome is given by the combinations of 5 that can be chosen from 52, as follows;
[tex]\displaystyle The \ \mathbf{number} \ of \ \mathbf{possible \ outcomes}} = _{52}C_5 = \frac{52!}{5! \cdot (52 - 5)!} = 2598960[/tex]
Therefore;
The statement; the total number possible outcomes is ₅₂C₅ is trueThird statement;
The number of ways of choosing two diamonds is found as follows;
[tex]\displaystyle Choosing \ two \ diamonds = _{13}C_2 = \mathbf{\frac{13!}{2! \cdot (13 - 2)!}} = 78[/tex]
The number of ways of choosing three hearts is found as follows;
[tex]\displaystyle Choosing \ three \ hearts = _{13}C_3 = \frac{13!}{3! \cdot (13 - 3)!} = 286[/tex]
The number of ways of choosing two diamonds and three hearts is found as follows;
[tex]\displaystyle Choosing \ two \ diamonds \ and \ three \ hearts = \frac{_{13}C_2 \times _{13}C_3}{_{52}C_5} = 0.00858[/tex]
Therefore, the number of ways of choosing two diamonds and three hearts ≠ 0.089
[tex]\displaystyle Choosing \ two \ diamonds \ and \ three \ hearts = \mathbf{\frac{_{13}C_2 \times _{13}C_3}{_{52}C_5}} \neq 0.089[/tex]
Fourth statement;
[tex]\displaystyle Probability \ of \ choosing \ five \ spades = \frac{_{13}C_5 }{_{52}C_5} \approx 0.0005[/tex]
Therefore;
[tex]\displaystyle Probability \ of \ choosing \ five \ spades = \mathbf{\frac{_{13}C_5 }{_{52}C_5}} \neq 0.05[/tex]
Fifth statement;
[tex]\displaystyle Probability \ of \ choosing \ five \ clubs= \frac{_{13}C_5 }{_{52}C_5} \approx 0.0005[/tex]
Therefore;
The statement, the probability of choosing five clubs is roughly 0.0005 is true.The possible question options in the question are;
The total possible outcomes is given by ₅₂C₅
The total possible outcomes is given by ₅₂P₅
Probability of choosing 3 hearts and 2 diamonds is 0.089
The likelihood of choosing 5 spades is approximately 0.05
The likelihood of choosing 5 clubs is approximately 0.0005
Learn more about combinations and probability here:
https://brainly.com/question/25718474
What is the length of the altitude of the equilateral triangle below?
Answer:
D 5sqrt(3)
Step-by-step explanation:
We can use the Pythagorean theorem to solve since the altitude is perpendicular to the base
a^2+b^2 = c^2
5^2 + a^2 = 10^2
25+a^2 = 100
a^2 =100-25
a^2 = 75
Taking the square root of each side
a = sqrt(75)
a = sqrt(25)sqrt(3)
a = 5sqrt(3)
Answer:
Step-by-step explanation:
D
Find the value of 8 to the 3rd power divided by 8 squared multiplied by 4 squared.
Answer:
0.5
Step-by-step explanation:
8^3 = 512
(8^2)*(4^2) = 1024
512/1024 = 0.5
20 is about what percent of 52
Answer:
To get the solution, we are looking for, we need to point out what we know.
1. We assume, that the number 52 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for.
3. If 52 is 100%, so we can write it down as 52=100%.
4. We know, that x is 20% of the output value, so we can write it down as x=20%.
5. Now we have two simple equations:
1) 52=100%
2) x=20%
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
52/x=100%/20%
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.
7. Solution for what is 20% of 52
52/x=100/20
(52/x)*x=(100/20)*x - we multiply both sides of the equation by x
52=5*x - we divide both sides of the equation by (5) to get x
52/5=x
10.4=x
x=10.4
now we have:
20% of 52=10.4
Step-by-step explanation:
can Julie win if she reads 8 books
Answer:
Yes, she can.
Step-by-step explanation:
12 < 5+8
Answer:
Step-by-step explanation:
No, she can't
Julie can't win because she has to read more than Emad so she has to read 13 books but she reads 8 books so she can't win
I hope it'll help you much
Thank you for asking
(−2)(−2)+4 is equal to
Answer:
8
Step-by-step explanation:
[-2][-2]=-2 x-2=4
4+4=8
Fred's birthday party will be in a room at the community center. The room can hold 75 people. He wants to use tables that seat 5 people each. Which inequality can be used to find the maximum number of tables, t, that Fred can use?
Answer:
75>5t
Step-by-step explanation:
Here is the information given:
75 is the maximum
5 per table
t is table
So, 75 is greater than or equal to the number of tables.
If 5 is the max seated at a table we know that it will be 5 people per table or 5t
Which gives us 75>5t
Furthermore, when solving we get t=15, when plugging this in the inequality becomes 75>75 which is true.
Hope this helps!
When a higher confidence level is used to estimate a proportion and all other factors involved are held constant
Options :
A) the confidence interval will be wider.
B) the confidence interval will be narrower.
C) there is not enough information to determine the effect on the confidence interval.
D) the confidence interval will be less likely to contain the parameter being estimated.
E) the confidence interval will not be affected.
Answer: A) The confidence interval will be wider
Step-by-step explanation: In statistics, When a higher confidence interval is used to estimate a proportion with other factors being held constant, the confidence interval will be wider. Since the confidence interval is aimed at tweaking the precision of our measurement or estimation, when we adopt a higher confidence level, we are trying g to reduce our chances of being wrong and hence increasing our precision and thus widening the level of confidence in the result obtained. That said, 95% confidence interval is wider than 90%. And 99% is wder than 95%.
Factor completely. 10x^3 + 2x^2 + 5x + 1
Answer:
(5x+1)(2x^2+1)
Step-by-step explanation:
Add and subtract the second term to the expression and factor by grouping.
Please Help Me i'll give you all my points
A survey of your friends find that 11 own a dog, 12 own a cat, and 7 have no pet. Find the experimental probability that the next person you ask will be a cat owner.
Answer:
40% chance or probability
Step-by-step explanation:
30 people total 12 have had a cat, convert into fraction, 6/15, convert into a percent and you get 40%
A triangle has vertices at A(-2,4), B(-2,8), and C(6,4). If A’ has coordinates of (-0.25,0.5) after the triangle has been dilated with a center of dilation about the origin, which statements are true? Check all that apply
Answer:
Now we need to find B' and C' by multiplying 0.125 with the x-coordinate and y-coordinate.
-----
x-coordinate of B is -2, y-coordinate of B is 8
x-coordinate of B'
y-coordinate of B'
So
-----
x-coordinate of C is 6 and y-coordinate of C is 4
x-coordinate of C'
y-coordinate of C'
So
Conclusion:
The below are the TRUE statements:
(i) The coordinates of C' are (0.75, 0.5)
(ii) The scale factor is 1/8
(iii) The coordinates of B' are (–0.25, 1).
Read more on Brainly.com - https://brainly.com/question/10679054#readmore
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
i got it correct
Prove algebraically that (image). Trigonometric Identities. Please help.
Answer:
Step-by-step explanation:
833 ÷ 64 showing remainders
Answer:
13.015625
Step-by-step explanation:
Answer:
13 remainder 1.
I have attached the work to your question.
Please see the attachment below.
I hope this helps!
To solve for 10t = -30 + 5t, first subtract ?
from both sides.
Answer:
-6
Step-by-step explanation:
10t = -30 + 5t, Inverse operations
'5t -5t. Subtract 5t from both sides
5t = -30. Divide by 5 both sides
/5. /5
t = -6
Ana is saving to buy a bicycle that costs $135. She has saved $98 and wants to know how much more money she needs to buy the bicycle.The equation 135 = x + 98 models this situation, where x represents the additional amount of money Ana needs to buy the bicycle... When substituting for x, which value(s), if any, from the set {0, 37, 98, 135, 233} will make the equation true? *
Answer:
37
Step-by-step explanation:
135-98 equals 37
O model the problem containing an unknown number, translate the statement into an equation. Sixteen is five less than a number. Which steps would you take to translate the statement? Replace "is" with =, "less than" with –, and "a number" with n to get 16 = 5 – n. Replace "is" with =, "less than" with +, and "a number" with n to get 16 = n + 5. Replace "is" with =, "less than" with –, and "a number" with n to get 16 = n – 5. Replace "is" with =, "less than" with ÷, and "a number" with n to get 16 = 5 ÷ n.
Answer:
Replace "is" with =, "less than" with –, and "a number" with n to get 16 = n – 5
Step-by-step explanation:
Hi, to answer this question we have to analyze the statement given and write an equation:
Sixteen is five less than a number
So, the number sixteen (16) is (=) five less (-5) than a number (n).
We have to subtract 5 to a number (x) and that expression must be equal to 16.
Mathematically speaking:
16= n-5
So, the correct option is:
Replace "is" with =, "less than" with –, and "a number" with n to get 16 = n – 5
Feel free to ask for more if needed or if you did not understand something.
Answer:
C :)
Step-by-step explanation:
before you go, don't forget to smile:)
An investor invested a total of $900 in two mutual funds. One fund earned a 7% profit while the other earned a 4% profit. If the investor's total profit was $51, how much was invested in each mutual fund? The amount invested in the mutual fund that earned 7% was?
Answer:
y = 400 (amt invested at 4%)
x = 500 (amt invested at 7%)
Step-by-step explanation:
Kindly check attached picture for detailed explanation
What is the experimental probability of not rolling a 2?
Answer:
5/6
Step-by-step explanation:
What is the product? 2y/y-13 * 4y-12/2y+6
Answer:
[tex]=\frac{4y}{y+3}[/tex]
Step-by-step explanation:
[tex]\frac{2y}{y-3}\cdot \frac{4y-12}{2y+6}\\\frac{4y-12}{2y+6}=\frac{2\left(y-3\right)}{y+3}\\\frac{4y-12}{2y+6}\\\mathrm{Factor}\:4y-12:\quad 4\left(y-3\right)\\4y-12\\\mathrm{Rewrite\:as}\\=4y-4\cdot \:3\\\mathrm{Factor\:out\:common\:term\:}4\\=4\left(y-3\right)\\=\frac{4\left(y-3\right)}{2y+6}\\\mathrm{Factor}\:2y+6:\quad 2\left(y+3\right)\\2y+6\\\mathrm{Rewrite\:as}\\=2y+2\cdot \:3\\\mathrm{Factor\:out\:common\:term\:}2\\=2\left(y+3\right)\\=\frac{4\left(y-3\right)}{2\left(y+3\right)}[/tex]
[tex]\mathrm{Divide\:the\:numbers:}\:\frac{4}{2}=2\\=\frac{2\left(y-3\right)}{\left(y+3\right)}\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=\frac{2\left(y-3\right)}{y+3}\\=\frac{2y}{y-3}\cdot \frac{2\left(y-3\right)}{y+3}\\\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\cdot \frac{c}{d}=\frac{a\:\cdot \:c}{b\:\cdot \:d}\\=\frac{2y\cdot \:2\left(y-3\right)}{\left(y-3\right)\left(y+3\right)}\\\mathrm{Cancel\:the\:common\:factor:}\:y-3\\=\frac{2y\cdot \:2}{y+3}[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:2\cdot \:2=4\\=\frac{4y}{y+3}[/tex]
Answer:
12/6
Step-by-step explanation:
HELPPPPPPP GIVING 100 POINTS FOR ANSWER.......Ivan bought a box of macadamia nuts to bring home from his trip. A rectangular prism with a length of 18 centimeters, width of 15 centimeters, and height of 3 centimeters. What volume of nuts could the container hold? 270 centimeters cubed 369 centimeters cubed 738 centimeters cubed 810 centimeters cubed
Answer:
18 x 15 x 3 is 810. The volume is 810.
Step-by-step explanation:
Volume of cuboid= Length*Width*Breadth
Volume of container= 18 cm X 15 cm X 3cm
Volume of container=810
Hope i helped
Answer:
[tex]810[/tex] centimeters cubed.
Step-by-step explanation:
The formula: [tex]Length * width * height[/tex]
[tex]18 *15*3 =810[/tex] centimeters cubed
what is char antonym?
Answer:
Antonyms. achromatic exhale spiny-finned fish extinguish hypopigmentation. Etymology.
Step-by-step explanation:
none but google
Answer:
If you mean char = a charred substance then you could have cool, extinguish, put out, smother, stifle or subdue.
Step-by-step explanation:
Google... everything's google
x - y = 3
a. work out the value of 5(x-y)
b. work out the value of 2x - 2y
c. work out the value of y - x
will give brainliest !
Please help it's due at 2:45!!!!!!!!
Answer:
5 (x-y)=15
2x-2y=6 and
y-x=-3
Step-by-step explanation:
first x-y=3, so you substitute x by y or y by X. anyway I substituted x by y. so x=y+3.
a. 5(x-y)
5[(y+3)-y] (first you substitute x by y+3.)
5 [y+3-y] ( then you remove the bracket.)
5[y-y+3] ( you collect like terms in the bracket.)
5 [3] (-y+y=0) so it means 5×3=15.
b. 2x-2y (like before you substitute x by y+3.)
2 (y+3)-2y
2y+6-2y (then you remove the bracket.)
2y-2y+6 (you collect like terms)
0+6=6. (because 2y-2y=0)
c. y-x
y-(y+3) ( you substitute x by y+3.)
y-y-3 (you remove the bracket)
0-3=-3 (because y-y=0)
The length, l, of a rectangle is 3 inches greater than its width, w. The perimeter of the rectangle is at least 30 inches. Which inequalityshows the range of possible lengths of the rectangle?
Answer:
l >= 9 and w >= 6
Step-by-step explanation:
The perimeter of the rectangle can be found by:
→ Perimeter = (2 x length) + (2 x width) (1)
Since the length is 3 inches greater than the width:
→ l = w + 3
Also, the perimeter is at least 30 inches
If you substitute the values in the equation 1:
→ (2 x l) + (2 x w) >= 30
→ (2 x (w + 3)) + (2 x w) >= 30
→ 2 x w + 6 + (2 x w) >= 30
→ 4 x w >= 24
→ w >= 6
Since l = w + 3, l >= 9
Correct answer only please!
To the nearest cent, how much will she have in 5 years?
Use the formula B = p(1 + r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Work Shown:
B = p*(1+r)^t
B = 4530*(1+0.11)^5
B = 7,633.313442603 approximately
B = 7633.31 round to the nearest cent
Kristen lives directly east of the park. The football field is directly south of the park. The library sits on the line formed between Kristen’s home and the football field at the exact point where an altitude to the right triangle formed by her home, the park, and the football field could be drawn. The library is 6 miles from her home. The football field is 7 miles from the library.
a. How far is library from the park?
b. How far is the park from the football field?
Answer:
a. 6.48 miles b. 9.54 miles
Step-by-step explanation:
a. 7/x=x/6
x^2=42
x=6.48
b. 13/x=x/7
x^2=91
x=9.54
Answer:
A. 6.48 miles
B. 9.54 miles
Step-by-step explanation:
hope this helps :-)
Miki tosses a coin 50 times, and the coin shows tails 28 times.
What is the experimental probability of Miki getting tails?
Answer:
28/50, or 56 percent.
Step-by-step explanation:
Divide the number of events (in this case it's tails) by the number of possible outcomes. This means to divide 28 by 50. Your answer will be 0.56. As a percent, this is 56 percent, which is the probability of the coin landing on tails.