Answer:
Length of each side of equilateral Traingle is 10.75 unitsStep-by-step explanation:
Given that area of an equilateral traingle 50 square units.
Let the length of side of equilateral traingle be 'x' units. To calculate length of each side we will use the formula of area of equilateral traingle:
[tex] \: \: { \underline { \boxed{\pmb { \sf{ \purple {Area_{(equilateral \: traingle)} = \dfrac{\sqrt 3}{4} \times (Side)^2}} }}}} \\ [/tex]
By substituting the values in above formula:
[tex]~[/tex]
[tex] : \implies \sf \: \: 50 = \dfrac{ \sqrt{3} }{4} \times {(x)}^{2} \\ \\ \\ : \implies \sf \: \: {(x)}^{2} = \dfrac{50 \times 4}{ \sqrt{3} } \\ \\ \\ : \implies \sf \: \: {(x)}^{2} = \dfrac{200}{ \sqrt{3} } \\ \\ \\ : \implies \sf \: \: x = \sqrt{ \dfrac{200}{ \sqrt{3} } } \\ \\ \\ : \implies \: \: { \boxed{\pmb{ \frak{ x = 10.75 \: units }}}}\\ \\ \\ [/tex]
Hence, Length of each side of equilateral Traingle is 10.75 unitsNatoshia's den is 4 feet longer than it is wide. If the den's area is 320 square feet, what are the dimensions of the room?
Dimensions : 16 x 20
Let the width be xthen the length: x + 4 area of rectangle = Length * Widthsolving steps:
(x+4)(x) = 320x² + 4x = 320x² + 4x - 320 = 0x² +20x -16x -320 = 0x(x + 20) -16(x+20) = 0(x-16)(x+20) = 0x = 16, -20x = 16 [ As length or width can never be negative ]So we found Width = 16 feet
Length:
16 + 420 feetAnswer:
width = 16 ft
length = 20 ft
Step-by-step explanation:
Let width = x
If the length is 4 ft longer than the width, then
⇒ length = x + 4
Area of a rectangle = width × length
Given:
area = 320width = xlength = x + 4Substituting these values into the equation for the area of a rectangle and solving for x:
⇒ 320 = x(x + 4)
⇒ 320 = x² + 4x
⇒ x² + 4x - 320 = 0
⇒ (x - 16)(x + 20) = 0
⇒ x = 16, -20
As distance is positive, then x = 16 only.
Therefore, width = 16 ft and length = 20 ft
Find the perimeter of the shape shown below.
perimeter = turn of the figure
P = 6 + 3 + 4 + 4 + 3 + 6 + 3 + 4 + 3 = 36
the triangle has 2 équal sides => isosceles
and 1 angle is 60° so the triangle is equilateral
he negative square root of 16 is -4. What is the square root of -16?
About the minus sign with 16, square root of -1 is an imaginary number i(iota). Also we know that square root of -16 will be multiplication of square root of -1 and square root of 16. So the final answer becomes, + or - 4i. Hope this helps
a A hole in the shape of a hemisphere is carved into each face of a cube. The holes are identical and centered at the centre of each face. The holes touch their neighbours at only one point. The cube has side 2. What is the diameter of each hole?
Diameter of each hemispheral holes = the diameter of a full sphere = side length of cube = 2 units.
What is a Hemisphere?A hemishpere is half of a sphere. Thus, two hemispheres makes one full sphere.
Given the image as shown below, since the identical hemispheral holes are centered at the center of each fce and they touch each other at only one point, it means that two hemisphere meet to make one full sphere.
Therefore, the diameter of a full sphere = side length of cube.
Thus, diameter of each hemispheral holes = the diameter of a full sphere = side length of cube = 2 units.
Learn more about hemisphere on:
https://brainly.com/question/9280450
This is urgent I really I need the answers
Thanks in advance
equation: 2y = 3x + 15
If cross y-axis, the x will be 0
2y = 3(0) + 15
2y = 15
y = 7.5
crosses y-axis at (0, 7.5)
(b)
P(-1,10), Q(3,4)
(i) gradient:
[tex]\sf \dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\rightarrow \sf \dfrac{4-10}{3--1}[/tex]
[tex]\rightarrow \sf \dfrac{-6}{4}[/tex]
[tex]\rightarrow \sf -1.5[/tex]
(ii) midpoint:
[tex]\sf (x_m, y_m) = (\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2})[/tex]
[tex]\rightarrow \sf (x_m, y_m) = (\dfrac{3-1}{2}, \dfrac{4+10}{2})[/tex]
[tex]\rightarrow \sf (x_m, y_m) = (1,7)[/tex]
Weir and Max put $75 in quarters and dimes in the box. There were 400 more dimes than quarters. How many coins of each type were there
Answer:
100 quarters = 2500 cents = $25
500 dimes = 5000 cents = $50
total = $75
Step-by-step explanation:
A local outdoor equipment store is being sold. The buyers are trying to estimate the percentage of items that are outdated. They will randomly sample among its 100,000 items in order to determine the proportion of merchandise that is outdated. The current owners have never determined their outdated percentage and can not help the buyers. Approximately how large a sample do the buyers need in order to insure that they are 98 % confident that the margin of error is within 3%
Using the z-distribution, as we are working with a proportion, it is found that the buyers need a sample of 1505.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In this problem, we have a 98% confidence level, hence[tex]\alpha = 0.98[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.98}{2} = 0.99[/tex], so the critical value is z = 2.327.
There is no estimate of the percentage, hence [tex]\pi = 0.5[/tex], and the margin of error is of M = 0.03, hence we solve for n to find the desired sample size.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 2.327\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.03\sqrt{n} = 2.327(0.5)[/tex]
[tex]\sqrt{n} = \frac{2.327(0.5)}{0.03}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{2.327(0.5)}{0.03}\right)^2[/tex]
[tex]n = 1504.2[/tex]
Rounding up, the buyers need a sample of 1505.
More can be learned about the z-distribution at https://brainly.com/question/25890103
Is the function in this table linear or nonlinear and why?
What is the surface area of the cylinder with height 8 and radius 2? Round your answer to the nearest thousandth.
Answer:
surface area of cylinder is 126cm²
Step-by-step explanation:
Height of a cylinder is 8cm
Radius of a cylinder is 2cm
surface area = ?
surface area of cylinder= 2πr(r + h)
=2×22/7×2(2+8)
=44/7×2(10)
=44/7×20
=880/7
=125.71
A = 2πrh + 2πr² π=3.14
(2 x 3.14 x 2 x 8) + (2 x 3.14 x 2x2)100.48 + 25.12A =125.6What is a line? What is an angle? How do you describe a line and an angle? How do we know if an angle is right? obtuse? acute? or a full circle?
Answer:
A line is something that goes on endlessly in both directions. An angle is the number of degrees at a point where two rays meet. We know if an angle is right if there is a right angle that measures up to 90°. An obtuse is any angle that measures over 90° and an acute angle is under 90°. Hope this helps! :)
Step-by-step explanation:
The school band sells carnations on Valentine's Day for $3 each. It buys the carnations from a florist for $0.50 each, plus a $15 delivery charge. When will the cost of the carnations be equal to the revenue from selling them? How many carnations does it need to sell to reach this point?
The cost of the carnations will be equal to the revenue when it has sold
_______ carnations. It will reach this point after it sells ______carnations.
Answer:
6 carnations
Step-by-step explanation:
0.5x +15 = 3x
x = 6
Help!!!!! This is i-ready !!! Will mark brainiest please help!!!!
Answer:
I think answer C
Step-by-step explanation:
You can display how many toothbrushes were distributed each month on the dot plot :)
Have an amazing day!!
Please rate and mark brainliest!!
HELP PLEASE
Find the area of the irregular figure.
5 in.
4 in
A = [ ? ]in.?
5 in.
9 in.
12 in.
4 in
5 in.
Answer:
Area of a rectangle
A = lw
Answer number 10 please. Thank you.
Given AB and AC are lines that are tangent to the circle with
the measure of angle BAC = 40°, what is the measure of angle BDC?
Answer:
C
Step-by-step explanation:
Givens
You are given 2 tangent lines.
You are also given a 4 sided figure.
All 4 sided figures have 360 degrees
A radius meets a tangent at 90 degrees
Formula
<BDA + <DCA + <BCA + <BDC = 360
Solution
90 + 90 +40 + <BDC = 360 Combine
220 + <BDC = 360 Subtract 220 from both sides
220- 220 +BDC =360 - 220
<BDC = 140
Answer: C
A store is having a clearance special and every item is 10% off. What is the sale price of a $310 suit?
Answer:
$279
Step-by-step explanation:
10% off $310 is $31
310-31 is 279
Answer: the sale price of the suit is $279 or $31 dollars off
Step-by-step explanation:
$310 x 0.10= $31
$310 - $31= $279
Mary walks to her garage. The distance to the garage as a function of time is shown in this graph
A. Mary starts 8 meters from the garage.
B. Mary walks 8 meters every 4 seconds.
C. Mary arrives at the garage after 4 seconds.
D. Mary walks at a speed of 2 meters per second.
Answer:
d
Step-by-step explanation:
so if you look at the bottom left corner you can see 1 box is the same as saying for every second someone walks its one metre.
thats not how i got the answer though.
if you look at the starting point at 8 because she was 8 meters away you need to see when she comes across her first second which after 2 meters (Goes down two squares before reaching the first second)
now technically soe of the other answers are correct too but heres how i thought about it.
A. its correct but i dont think that's what its asking you for tbh
B. This we don't know for sure. eg she could take 890 seconds walking back to her starting point we just don't know for sure.
C. This is also true but once again it's easily given to you so i dont think that's what you're being asked.
D. This is the only option where you had to do any for of working out because s=d/t so s=8/4=2m/s
The question is in the attachment!!
[tex] \qquad\quad\hookrightarrow{\sf { 1000(e-1)}}[/tex]
Solution:[tex] \begin{aligned}&\longrightarrow \int_{0} ^{1000} {e}^{ - |x| }dx = \sum_{k = 0}^{999} \int_{k}^{k + 1}e ^{x - |x| }dx \\ \\ &\longrightarrow\int_{0} ^{1000} {e}^{ - |x| }dx = \sum_{k = 0}^{999} \int_{k}^{k + 1}e^{x - k}dx \\\\&\longrightarrow\int_{0} ^{1000} {e}^{ - |x| }dx = \sum_{k = 0}^{999}e^{x - k \big |_{k}^ {k + 1}} \\ \\& \longrightarrow\int_{0} ^{1000} {e}^{ - |x| }dx = \sum_{k = 0}^ {999}(e - 1)\\\\&\longrightarrow\int_{0} ^{1000} {e}^{ - |x| }dx = 1000(e - 1)\end{aligned}[/tex]
help please
What is the surface area of a cube with an edge of 5 cm?
Answer:
150 cm^2
Step-by-step explanation:
A cube has 6 surfaces
Each surface square = 5 by 5
So.....
5 x 5 (or 25) times 6
25 x 6 = 150
Hope this helps!
In Juneau, Alaska, the 30-year annual snowfall average is 86. 7 inches with a standard deviation of 40. 4 inches. The last four years saw an average annual snowfall of 115. 7 inches, 62. 9 inches, 168. 5 inches, and 135. 7 inches. Hia performs a hypothesis test on this data to determine if the next 30-year norm will have a different average if the trend from the last four years continues. She uses a significance level of 5%. Which of the following is a conclusion that she may make? The z-statistic is 1. 44, so the null hypothesis cannot be rejected. The z-statistic is 1. 68, so the null hypothesis cannot be rejected. The z-statistic is 1. 85, so the null hypothesis should be rejected. The z-statistic is 4. 6, so the null hypothesis should be rejected.
The z-statistic is 1. 68, so the null hypothesis cannot be rejected.
What is null hypothesis?The expected value of the amount of average snowfall for over 30 years is 86.7 inches with a standard deviation of 40.4 inches.
To verify if this particular trend continues, we must check the significance value of the amount snowfall for the past four years.
Given that the snowfall for past years are as follows: 115.7 inches, 62.9 inches, 168.5 inches, and 135.7 inches.
Thus the mean of the sample would be: (115.7 + 62.9 + 168.5 + 135.7)/4 = 120.7 inches.
To compute for the z-score,
we have z-score = (x – μ) / (σ / √n)
where x is the computed/measured value,
μ is the expected mean, σ is the standard deviation,
and n is the number of samples.
Using the information we have,
z-score (z) = (120.7 - 86.7) / (40.4/ √4) = 1.68
In order to reject the null hyptohesis our probability value must be less than the significance level of 5%. For our case, since z = 1.68, P-value = 0.093 > 0.05.
Hence The z-statistic is 1. 68, so the null hypothesis cannot be rejected.
To know more about Null hypothesis follow
https://brainly.com/question/15980493
Answer:
B. The z-statistic is 1.68, so the null hypothesis cannot be rejected.
Step-by-step explanation:
edg 22, got 100 on unit test
answer the question with true or false:
Answer:
true
Step-by-step explanation:
SOMEONE PLSLPLSSLSLS HELP ITS JUST 3 QUESTIONS BRO PLEASE ITS SO CONFUSING ILL BRAINLIST.
The length and width of a rectangle is 3x + 4 and x + 3 respectively.
a) write the perimeter of the rectangle in simplified form.
b) find the perimeter of the rectangle if x = 5.
c) the area of a rectangle is given by the formula area = length x width. Find the area of this rectangle when x = 4.
Step-by-step explanation:
a) Perimeter is equal to 2w + 2L
2(3x + 4) + 2(x + 3)
6x + 8 + 2x + 6
8x + 14
b) Put 5 in x's place
8×5 + 14
40 + 14
54
c) Area = (3x + 4) * (x + 3)
Put 4 in x's place
(3×4 + 4) * (4 + 3)
12 + 4 * 7
16 * 7
112
x = –8 –6x + 9y = 12 solve for substitution
Answer:
x= -8,y= -4
Step-by-step explanation:
Substitute x= -8
-6(-8)+9y=12
simplify
48+9y=12
isolate for y
y= -4
The solutions to the system of equations are:
x= -8 and y= -4
The figure below is composed of eight circles, seven small circles and one large circle containing them all. Neighboring circles only share one point, and two regions between the smaller circles have been shaded. Each small circle has a radius of 5 cm.
The figure below is composed of eight circles, seven small circles and one large circle containing them all. Neighboring circles only share one point, and two regions between the smaller circles have been shaded. Each small circle has a radius of 5 cm.
What is the volume of this figure?
Enter your answer in the box.
ft³
Answer:
96
Step-by-step explanation:
L=6
W=2
H=8
LxWxH=8x6x2=96
8x6=48
48x2=96
Answer:
76
Step-by-step explanation:
the answer is 76 because I took the test
Sydney read 50 pages in 40 minutes. She reads at a constant rate.
How many pages can Sydney read per minute
Answer:
divide the number of pages by the time
Step-by-step explanation:
=50/40
=5/4
= 1.25/per minute
The water level at a lake is normally O feet above
sea level. During a flood, the level rose 7 feet. Over
the next two weeks the level had gone down by
12 feet.
a. Write an expression to represent this situation.
b. What level is the water currently at?
Miki, a resident of kyoto, earns an annual salary of ¥6,760,950. if the japanese government levies a 29.12% income tax on miki’s tax bracket, what is her yearly take-home pay, to the nearest whole yen? a. ¥4,792,161 b. ¥4,643,510 c. ¥4,439,195 d. ¥4,364,869
The amount of yearly take-home pay of Miki, a resident of Kyoto after the payment of income tax is ¥4,792,161.
What do you mean by percentage?
Percentage of a number is the part of the number expressed in the in every hundred. Percentage of a number is expressed with the percentage symbol '%'.
Miki, a resident of kyoto, earns an annual salary of ¥6,760,950. The Japanese government levies a 29.12% income tax on miki’s tax bracket.
The amount of tax Miki pay to the government as income tax is,
[tex]I=\dfrac{29.12}{100}\times6760950\\I=1968788.64[/tex]
Miki, earns an annual salary of ¥6,760,950. Thus, her yearly take-home pay after the deduction of income tax is,
[tex]M=6760950-1968788.64\\M=4792161.36\\M\approx4792161[/tex]
Thus, the amount of yearly take-home pay of Miki, a resident of Kyoto after the payment of income tax is ¥4,792,161.
Learn more about the percentage here;
https://brainly.com/question/24304697
Answer:
A
Step-by-step explanation:
:) good luck
Which value should she use as the common ratio?
0.05
0.5
1.05
5.0
Answer:
0.5
Step-by-step explanation:
0.5
I guess i am 70% sure
In the rectangle below, sketch the position of the ribbons and outline a right triangle with a diagonal of the rectangle as the hypotenuse. Then, label the right triangle below the rectangle with the appropriate lengths from the problem.
The length of the ribbon needed to cross from one corner of the rectangle to the other corner is 7 1/2 feet.
What is the length of the ribbon needed?The length of the ribbon needed can be determined using the Pythagoras theorem.
The Pythagoras theorem: a² + b² = c²
where
a = length
b = base
c = hypotenuse
√4.5² + 6²
√36 + 20.25 = 7.5 feet
To learn more about Pythagoras theorem, please check: https://brainly.com/question/14580675