Answer:
Sum of diagonals = 20 units
Step-by-step explanation:
[tex]A(rectangle)=25\sqrt 3\: units^2\\w(rectangle) =5\: units[/tex]
To find: Sum of diagonals
[tex]A(rectangle)=l(rectangle)\times w(rectangle) [/tex]
[tex]\implies l(rectangle)=\frac{A(rectangle)}{w(rectangle)}[/tex]
[tex]\implies l(rectangle)=\frac{25\sqrt 3}{5}[/tex]
[tex]\implies l(rectangle)={5\sqrt 3}\: units[/tex]
Let the diagonals of the rectangle be [tex]d_1\:\&\:d_2\: units[/tex]
Diagonals of a rectangle are equal in measure.
[tex]\implies d_1=d_2=\sqrt{l(rectangle)^2+w(rectangle)^2}[/tex]
(By Pythagoras Theorem)
[tex]\implies d_1=d_2=\sqrt{(5\sqrt 3)^2+(5)^2}[/tex]
[tex]\implies d_1=d_2=\sqrt{75+25}[/tex]
[tex]\implies d_1=d_2=\sqrt{100}[/tex]
[tex]\implies d_1=d_2=10\: units[/tex]
[tex]Sum \:of \:diagonals = d_1+d_2[/tex]
[tex]\implies Sum \:of \:diagonals = 10+10[/tex]
[tex]\implies Sum \:of \:diagonals = 20\: units[/tex]
Find the volume of the sphere.
Either enter an exact answer in terms of pi or use 3.14 for pi and round your final answer to the nearest hundredth
radius=8
The volume of a sphere with radius 8 units is 2143.57 units³
What is a Sphere?
A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center. It has surface area and volume based on its radius. It does not have any faces, corners or edges.
The Surface Area of a Sphere = 4πr²
The Volume of a Sphere = ( 4/3 ) πr³
where r is the radius of the sphere
Given data ,
Let the volume of the sphere be represented as A
Now , the value of A is
Let the radius of the sphere be r
The value of r = 8
Now , the formula to calculate the volume of the sphere is
Volume of a Sphere = ( 4/3 ) πr³
Substituting the values in the equation , we get
Volume of a Sphere = ( 4/3 ) x 3.14 x 8 x 8 x 8
Volume of a Sphere = ( 4/3 ) x 3.14 x 512
Volume of a Sphere = ( 4/3 ) x 1607.68
Volume of a Sphere = 2143.57 units³
Therefore , the value of A is 2143.57 units³
Hence , the volume of the sphere is 2143.57 units³
To learn more about sphere click :
https://brainly.com/question/27933834
#SPJ2
What is mZLKB?
A
65°
K
#
#
B
L
Answer:
65
Step-by-step explanation:
I got it right on my test!
The points (8, 0), (0, 9), (0, 0), and (6, 5) are the vertices of a feasible region for a linear programming problem. The objective function for the problem is C = 1.5x + 3.5y. Which point is the maximum value of C?
Answer:
the point 6,5 is the maximum Value of c out of the other points
Henri's balance in his savings account was $12,000. The savings
account earns annual simple interest. At the end of four years, the
balance of the account was $13,536. If Henri did not make any
additional deposits or withdrawals during this time, what was the
annual interest rate on this savings account?
18
Answer:
3.2%
Step-by-step explanation:
I = prt
I = $13,536 - $12,000 = $1,536
1,536 = 12,000 × r × 4
r = 1,536/(12,000 × 4)
r = 0.032 = 3.2%
EVALUATE: -2x-24 WHEN X = 2 AND y = 4.
Answer:
-28
Step-by-step explanation:
-2x-24
-2(2)-24
-4-24
-28
what equals 5 in multiplication and -4 in addition
Answer:
-2 +i-2 -iStep-by-step explanation:
There is no pair of real numbers that have a total of -4 and a product of 5. The complex numbers (-2+i) and (-2-i) will meet your requirements.
__
If the numbers of interest are 'a' and 'b', they will be zeros of the quadratic whose factored form is ...
(x -a)(x -b) = 0
Expanding that, we find an opportunity to use the given sum and product numbers:
x² -(a+b)x +ab = 0
x² -(-4)x +5 = 0
Rewriting this in vertex form gives ...
(x² +4x +4) +1 = 0
(x +2)² +1 = 0
We can find the values of x by subtracting 1 and taking the square root.
(x +2)² = -1
x +2 = ±√(-1) = ±i
x = -2±i
The two numbers of interest are -2+i and -2-i.
The local pool must hold a minimum of 12,000 gallons of water. The pool already has 8,000 gallons of water in it and is being filled at a rate of 250 gallons per hour. Drag the solution to the number line to show how many hours it will take to fill the pool with water to its minimum amount required.
Answer:
16 hours
Step-by-step explanation:
Remaining gallons to be filled :
Minimum water - Containing water12,000 - 8,0004,000 gallonsTime to fill 4,000 gallons
Amount to be filled / filling rate4,000 / 25016 hoursAnswer:
Step-by-step explanation:
This is the answer
Which of 2/5 or 5/8
is closer in value to 1/2?
Answer:
Step-by-step explanation:
Members of a baseball team raised $1386.50 to go to a tournament. They rented a bus for $1137.50 and budgeted $20.75 per player for meals. Determine the number of players the team can bring to the tournament.
Answer:
12 players
Step-by-step explanation:
the team started off with $1386.50
subtract $1137.50 for the rented bus
[tex]1386.50 - 1137.50 = 249[/tex]
the team has $249 left for the meals and a meal costs $20.75 for each player.
249 ÷ 20.75 = 12
the team can bring 12 players to the tournament.
Which is closest to the weight of 1 raisin box?
250 grams
84 grams
125 grams
42 grams
Step-by-step explanation:
answer 42 grams.
since total is 250 with 4 box combined. then , 250/4 = 42.25. which is approximately 42 grams
Identify the slope and y-intercept of each of the following lines. Then graph each line.
y + 3 = 2 (x + 4)
Answer:
Below!
Step-by-step explanation:
1. Determining the y-intercept of the line:
The provided equation is in point slope form. To determine the slope and the y-intercept, we need to convert the equation to slope intercept form. Once it is converted to slope intercept form, the constant will be the y-intercept of the line. Start out by simplifying the distributive property on the R.H.S.
[tex]\implies y + 3 = 2 (x + 4)[/tex]
[tex]\implies y + 3 = (2x + 8)[/tex]
Now, open the parenthesis on the R.H.S
[tex]\implies y + 3 = 2x + 8[/tex]
If we take a look at the formula of slope intercept form (y = mx + b), we can see that "y" is isolated on the L.H.S. Thus, we need to subtract 3 both sides to isolate the y-variable.
[tex]\implies y + 3 - 3 = 2x + 8 - 3[/tex]
[tex]\implies y = 2x + 5[/tex]
We can see that the only constant in the equation is 5.
Therefore, 5 is the y-intercept.
2. Determining the slope of the line:
To determine the slope of the line, let's compare the formula with the equation obtained.
[tex]\implies (y = 2x + 5) \ = \ (y = mx + b)[/tex]
Thus, we obtain the following:
y = y2 = m (Slope)x = x 5 = b (Y-intercept)Thus, 2 is the slope of the line.
3. Plotting the line on the coordinate plane:
To graph the line on a coordinate plane, plot the y-intercept on the graph. The y-intercept is ALWAYS plotted on the y-axis.
Thus, the y-intercept plotted on graph is (0, 5).
Furthermore, plot a second point on the graph to draw a straight line through those points.
Determining the second point of the line:
If the slope of the line is 2, it means that the run (x) is 1 and the rise (y) is 2. Thus, we can add 1 to the x-coordinate of the y-intercept and 2 to the y-coordinate of the y-intercept.
⇒ (0, 5) ⇒ x = 0; y = 5 ⇒ Second point: x = 0 + 1; y = 5 + 2⇒ Second point: x = 1; y = 7⇒ Second point: (1, 7)Then, plot these points on the coordinate plane. Keep in mind that plot the x coordinate first, then the y-coordinate next. Once the coordinates are plotted, draw a line from the x-coordinate and another line from the y-coordinate. Finally, use your ruler and draw a line that passes through those two points. Your obtained graph is the graph of the line.
Comapre to slope intercept form y=mx+b
Slope=m=2Y intercept=b=5Adrianna is making flower bouquets. She has 60 roses and 80 daisies. If Adrianna wants to make all the arrangements identical and have no flowers left over, how many roses will be in each bouquet?
Answer:
3
Step-by-step explanation:
60/3=20
80/4=20
Adrianna can make 20 bouquets with 3 roses and 4 daisies each.
30 POINTS NEED HELP ASAP IN CLASS HURRY!!
Answer:
5. -6/4
6. 1/2
7. 12/15
8. -21/8
Step-by-step explanation:
Steps are in picture
Answer:
Step-by-step explanation:
Fraction division:
Use KCF method
K - Keep the first fraction
C - Change division to multiplcation
F - Flip the second fraction
[tex]5) \dfrac{-6}{11} \div \dfrac{4}{11}=\dfrac{-6}{11}*\dfrac{11}{4}[/tex]
[tex]= \dfrac{-3}{2}\\\\= -1\dfrac{1}{2}[/tex]
[tex]6) 1\dfrac{1}{6} \div 2\dfrac{1}{3}=\dfrac{7}{6} \div \dfrac{7}{3}[/tex]
[tex]= \dfrac{7}{6}*\dfrac{3}{7}\\\\= \dfrac{1}{2}[/tex]
[tex]7) -4\dfrac{1}{5} \div -1\dfrac{3}{4}=\dfrac{-21}{5} \div \dfrac{-7}{4}[/tex]
[tex]=\dfrac{-21}{5}*\dfrac{4}{-7}\\\\= \dfrac{3}{5}*\dfrac{4}{1}\\\\=\dfrac{12}{5}\\\\=2\dfrac{2}{5}[/tex]
[tex]8) -6\dfrac{1}{8} \div \dfrac{7}{3}=\dfrac{-49}{8} \div \dfrac{7}{3}[/tex]
[tex]= \dfrac{-49}{8}*\dfrac{3}{7}\\\\= \dfrac{-7}{8}*\dfrac{3}{1}\\\\=\dfrac{-21}{8}\\\\=-2\dfrac{5}{8}[/tex]
Which three measures could be the side lengths of a right triangle? Explain or show your reasoning
SOMEONE PLEASE HELP ME WITH THIS ILL GIVE YOU BRAINLIST ANSWER
IMAGE ABOVE
Answer:
Step-by-step explanation:
.
Answer:
[tex]( \sqrt{24} ) ^{2} + 5 {}^{2} = 7 {}^{2} \\ [/tex]
Pythagoras theorem:
a²+b² = c²
where a, b and c are the adjacent, opposite sides and hypotenuse of a right angled triangle respectively.
Therefore, √24 , 5 and 7 are the sides of a right angled triangle.
2x+20+3x-5=180 ??need answer
Answer:
33
Step-by-step explanation:
2x+3x+20-5=180
5x+15=180
5x=180-15
5x=165
165/5=33
Donald writes 6 x 9 = 54. Explain two strategies you could use to check his work.
A. -25
B. 15
C. 25
D. 40
E. 65
Answer:
E.65
Step-by-step explanation:
Kimaya guesses that 11 is the mean of this data set. 8, 7, 11, 7, 6,`12 Without calculating, determine if Kimaya's guess could be correct.
Answer:
you add up the number and then take that answer and multiply that. with the nuber alone
Step-by-step explanation:
add up 8 7 11 6. 12 and then multiply that answer by 11. how to do it..... 8+7+11+6+12 =? 11×?=
Can I have help on this? I will award brainliest for the correct answer.
Answer:
7x(x+4)
Step-by-step explanation:
i got answer from mathay
Im so lost what the answer is
Answer:
Unfortunately, we can't do anything with 41 as it has no factors. Since [tex]3\sqrt{41}[/tex] is already simplified, try submitting that as your answer. If that doesn't work then try un-doing their steps and get rid of the 3:
[tex]3\sqrt{41}[/tex]
[tex]\sqrt{41(9)}[/tex]
[tex]\sqrt{369}[/tex]
Hope this helps!
Which expression represents the volume of the prism, in cubic centimeters? 9x2 7x 14x2 7x 16x2 14x 28x2 14x
Answer:
The answer is B
Step-by-step explanation:
Answer: b
Step-by-step explanation:
PLEASEEEE HELPPP I’m BEGGINGGG
When solving the following equation by completing the square, what would be your
first step?
x^2 - 6x – 40 = 0
Answer: Add 40 to both sides to collect like terms on each side of the equation
Step-by-step explanation: That's the first step
What is the minimum number of triangles needed to construct a hexagon? a hexagon. 3 4 5 6
Answer:
6
Step-by-step explanation:
draw a model and fit in some traingles
Answer:
it’s B :)
Step-by-step explanation:
give a that is if u think my dog is cute
HELP PLEASE
A parking lot charges $7 per day to park on weekdays and $12 per day on weekends.
Jamal parked his car in this lot on 6 days last week and spent a total of $52. How many
weekdays and weekend days did Jamal park?
Answer:
4 weekdays and 2 weekends.
Step-by-step explanation:
6 days.
x = weekdays
y = weekends
7x = amount with weekdays
12y = amount with weekends
7x + 12y = 52, total
x + y = 6, amount of days
solve double variable equation
x = 6 - y, plug in to 1st equation
7(6 - y) + 12y = 52
42 - 7y + 12y = 52
5y = 10
y = 2 weekends
2 + x = 6
x = 4 weekdays
Solve the distance from the ground station to the satellite.
Need Quick!!!
Apply Pythagorean theorem
H²=P²+B²H²=6371²+42157²H²=40589686+1777212649H²=1817802335H=42635km(Approx)Determining Whether a Difference Is Statistically Significant
You calculated the standard deviation of the sample mean differences to be 0.69. You also calculated the sample mean difference to be 1.74. Now you’ll determine whether the difference is significant. For the purpose of constructing the confidence interval, assume that there’s no difference between the population means.
Part A
Determine the 95% confidence interval for the difference of the sample means. Then complete the statements.
The 95% confidence interval is __ to ___ .
Blank 1: -1.26, -1.38, -3.48, -3.44
Blank 2: 3.44, 3.48, 1.38, 1.26
Part B
Which statement is true about the difference of the sample means?
1. The difference of the sample means is not statistically significant because it falls outside the 5% significance level.
2. The difference of the sample means is statistically significant because it falls outside the 5% significance level.
3. The difference of the sample means is not statistically significant because it falls within the 5% significance level.
4. The difference of the sample means is statistically significant because it falls within the 5% significance level.
Part C
What can you conclude about the color of the L-Bow Roni box?
The difference of the sample means is statistically significant because it falls outside the 5% significance level.
How to explain the statisticsThe formula for a 95% confidence interval for the difference between two population means is:
(sample mean difference) ± (critical value) x (standard error of the mean difference)
Assuming a two-tailed test and a sample size greater than 30, the critical value is approximately 1.96. The standard error of the mean difference is calculated by dividing the standard deviation of the sample mean differences by the square root of the sample size.
So, the 95% confidence interval is:
1.74 ± 1.96 x (0.69/√n)
Assuming that the sample size is not given, we cannot calculate the exact confidence interval. However, we can say that the confidence interval will be of the form:
1.74 ± (some number)
Therefore, the 95% confidence interval is a range of values that contains the true population mean difference with 95% confidence.
Blank 1: -1.26
Blank 2: 3.44
In order to determine whether the difference is statistically significant, we need to compare the confidence interval to the null hypothesis of no difference. If the confidence interval does not contain the null hypothesis value, then we can reject the null hypothesis and conclude that the difference is statistically significant at the chosen significance level (5% in this case).
The null hypothesis in this case is that there is no difference between the population means. Since we are assuming this for the purpose of constructing the confidence interval, the null hypothesis value is 0.
The confidence interval in Part A does not contain the null hypothesis value of 0, since it ranges from -1.26 to 3.44. Therefore, we can reject the null hypothesis and conclude that the difference is statistically significant at the 5% significance level.
So, the correct answer is that the difference of the sample means is statistically significant because it falls outside the 5% significance level.
Learn more about confidence interval on
https://brainly.com/question/15712887
#SPJ1
I need help with this question
Answer:
[tex]\frac{1}{12}[/tex]
Step-by-step explanation:
The probability of picking a 3 is 1/4.
The probability of picking up a 1 the second time will be 1/3 since there will only be 3 cards left after the first time picking up the 3.
So 1/4 x 1/3 = 1/12
yolanda makes wooden boxes for a crafts fair. She makes 25 boxes like the one shown, and she wants to paint all the outside faces. What is the surface area of all 25 boxes?
1550 sq. in
hope it helps..!!!
Graph this parabola
Please show all steps thank you!!!
Vertex form of parabola
y=a(x-h)²+kFrom the equation given
Vertex=(h,k)=(3,4)a=-2As a is negative parabola facing downwards
Graph attached
A trapezoidal sum is an underestimate when the function is.
Answer: Concave down
Explanation:
An example is shown below. We have the concave down parabola [tex]y = -x^2+7[/tex] marked in red. The trapezoidal sum is in blue. The three trapezoids combine to something just a bit smaller than the true area under the curve from x = -2 to x = 1. Therefore, this trapezoidal sum is an underestimate of the true area under the curve.
Every part of each trapezoid is completely below the red curve. In other words, no part of the blue pieces spill above the parabola.