Answer:
[tex]x=\frac{1}{4}h-\frac{1}{2} -3y[/tex]
Step-by-step explanation:
[tex]h = 4 ( x + 3y ) + 2[/tex]
[tex]h-2=4(x+3y)[/tex]
[tex]4(x+3y)=h-2[/tex]
[tex]x+3y=\frac{h-2}{4}[/tex]
[tex]x=\frac{h-2}{4}-3y[/tex]
In ΔIJK, the measure of ∠K=90°, IK = 9, JI = 41, and KJ = 40. What ratio represents the sine of ∠I?
Answer:
The ratio is 40/41
Step-by-step explanation:
In this question, we are to find the ratio that represents sine of angle I
Firstly, let’s consider the diagram of the triangle attached.
When we talk of sine, what we mean is the trigonometric identity which measures the ratio of the opposite to the hypotenuse.
Since the angle we are considering is I, the opposite is 40, while the hypotenuse is 41 ( the longest side of the triangle and the side that faces the angle 90, which is the length JI)
Thus,
mathematically sine I = 40/41
Answer:
Step-by-step explanation:
Identify the vertex of the function, fx) = 3(x - 1)2 + 5.
Answer:
fx) = [tex]3x+4[/tex]
Step-by-step explanation:
1. step:
solve the bracket
fx) = 3([tex]x[/tex] - 1) 2 + 5
[tex]fx) = 3x-1+2+5[/tex]
2. step:
use the BEDMAS form.
fx) = [tex]3x-3+7[/tex]
fx) = [tex]3x+4[/tex]
Which represents the solution(s) of the system of equations, y = –x2 + 6x + 16 and y = –4x + 37? Determine the solution set algebraically.
Answer:
The equations had 2 solutions:
x = 3, y = 25 or x = 7, y = 9
Step-by-step explanation:
(x - 6) x + y = 16, 4 x + y = 37
y = 37 - 4 x
x2-6x+37-4x-16=0
x2-10x+21=0
(x - 7) (x - 3) = 0 -> x =3 or x = 7
Answer:
C. is right on edg.
A trapezoid has a height of 8 meters, a base length of 12 meters, and an area of
64 square meters. What is the length of the other base?
The length of the other base is 4 meters.
What is a trapezium?It is a quadrilateral that has one pair of parallel sides and a height.
The area is calculated as 1/2 x the sum of the parallel sides x height.
Examples:
Area of a trapezium that has the parallel sides as 3 cm and 4 cm and a heght o 5 cm.
Area = 1/2 x (3 + 4) x 5
Area = 1/2 x 7 x 5
Area = 35/2 = 17.5 cm^2
We have,
The area of a trapezoid.
A = (1/2) h (b1 + b2)
where A is the area, h is the height, b1, and b2 are the lengths of the two bases.
We are given,
h = 8, b1 = 12, and A = 64.
We can substitute these values into the formula and solve for b2:
64 = (1/2)(8)(12 + b2)
Simplifying:
64 = 4(12 + b2)
16 = 12 + b2
b2 = 4
Therefore,
The length of the other base is 4 meters.
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Given: PQRS is a rectangle. Put a checkmark in every box that must be true. You will put more than one checkmark. Use calculations and words to show this quadrilateral meets the definition of a kite.
Answer:
The true options are:
2) Has exactly one pair of parallel sides
4) Has exactly one pair of congruent sides
5) Both pairs of opposite sides are congruent
7) There are right angles at all 4 vertices
9) The diagonals are congruent
10) The diagonals bisect each other.
How to solve -5 + 13y = -7
Answer:
y = -2/13
Step-by-step explanation:
-5 + 13y = -7
Add 5 to each side
-5+5 + 13y = -7+5
13y = -2
Divide by 13
13y/13 = -2/13
y = -2/13
A car is traveling at a speed of 72 kilometers per hour. What is the cars speed in kilometers per minute? How many kilometers will the car travel in 10mins?
Answer:
1.2 kilometers per minute; 12 kilometers
Step-by-step explanation:
We know that 60 minutes makes 1 hour.
Therefore, to convert the speed to kilometers per minute, we simply divide 72 kilometers per hour by 60 minutes:
72 / 60 = 1.2 kilometers per minute.
Distance is given as speed multiplied by time.
Therefore, in 10 mins, the car travels:
1.2 * 10 = 12 kilometers.
The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.7 days and a standard deviation of 2.4 days. What is the 90th percentile for recovery times? (Round your answer to two decimal places.)
Answer: the 90th percentile for recovery times is 8.77 days.
Step-by-step explanation:
Let x be the random variable representing the recovery time of patients from a particular surgical procedure. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
From the information given,
µ = 5.7 days
σ = 2.4 days
The probability for the 90th percentile is 90/100 = 0.9
The z score corresponding to the probability value on the normal distribution table is 1.28
Therefore,
1.28 = (x - 5.7)/2.4
Cross multiplying, it becomes
1.28 × 2.4 = x - 5.7
3.072 = x - 5.7
x = 3.072 + 5.7 = 8.77 days
If lines p and q are parallel then the value of x is
Answer:
The answer is A. 10
Step-by-step explanation:
The two angles are alternate interior angles so they are congruent. Since they are congruent, you can write it in an equation.
5x - 25 = 3x - 5
subtract 3x from each side
2x - 25 = -5
add 25 to each side
2x = 20
divide 2 from each side
x = 10
Also, if you want to check your answer, you can plug 10 back into the equation to see if they're equal.
The relation between the given angles is given by the alternate interior
angles theorem.
If lines p and q are parallel then the value of x is A. 10°
Reason:
The given parameters are;
Condition; Line p, and line q, are parallel.
The angles (3·x - 5)° and (5·x - 25)° are alternate interior angles.
According to alternate interior angles theorem, we have the alternate
angles are congruent, where line p, and line q are parallel.
Therefore;
(3·x - 5)° ≅ (5·x - 25)° By alternate interior angles
(3·x - 5)° = (5·x - 25)° By definition of congruency
Solving, we get;
(3·x - 5)° + 25° = (5·x - 25)° + 25°
3·x + 20° - 3·x = 5·x - 3·x = 2·x
20° = 2·x
[tex]x = \dfrac{20^{\circ}}{2} = 10^{\circ}[/tex]
The correct option is A. 10°
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Please help me with my math question!!
Which statements about experimental probability are true?
Experimental probability is written as a ratio.
Experimental probability includes the number of possible outcomes.
Experimental probability is found by conducting trials of an experiment.
Experimental probability includes the number of times an event occurs in the numerator, and the total number of trials in the denominator.
Experimental probability includes the number of times an event occurs in the denominator, and the total number of trials in the numerator.
Answer:
free points
Step-by-step explanation:
first, third, and fourth options
Answer:
1,3,4
Step-by-step explanation:
e2020
What is the next term in the sequence?
1,-3,9,-27
Begin by studying the pattern.
Here, notice that 1 × -3 is equal to -3.
-3 × -3 is equal to 9.
9 × -3 is equal to -27.
Continuing the same pattern, -27 × -3 is equal to 1.
So the next term in the pattern is 81.
So, we multiply by -3 each time.
Below are the jersey numbers of 11 players randomly selected from a football team. Find the range, variance, and standard deviation for the given sample data. What do the results tell us? 83 45 80 53 46 24 79 34 55 10 44 Rangeequals 73 (Round to one decimal place as needed.) Sample standard deviationequals 23.4 (Round to one decimal place as needed.) Sample varianceequals 547.2 (Round to one decimal place as needed.) What do the results tell us? A. The sample standard deviation is too large in comparison to the range. B. Jersey numbers are nominal data that are just replacements for names, so the resulting statistics are meaningless. C. Jersey numbers on a football team do not vary as much as expected. D. Jersey numbers on a football team vary much more than expected.
Answer: B. Jersey numbers are nominal data that are just replacements for names, so the resulting statistics are meaningless.
Step-by-step explanation:
Given the following list of data:
83 45 80 53 46 24 79 34 55 10 44
Range :
(Highest - Lowest) value
83 - 10 = 73
Sample Variance :
[Summation of (x - mean)^2] / number of observation - 1
Mean = (83+45+80+53+46+24+79+34+55+10+44) / 11
= 553 / 11 = 50.3
Check attached picture for computation of variance and standard deviation.
In football, jersey numbers do not imply any statistical relevance or importance
4
Find the arc length of the partial circle.
Either enter an exact answer in terms of or
use 3.14 for and enter your answer as a
decimal.
units
Answer:
12.56
Step-by-step explanation:
The arc length of the partial circle is L = 18.849 units
What is Central Angle?The central angle is an angle with two arms and a vertex in the middle of a circle. The two arms of the circle's two radii intersect the circle's arc at two separate locations. It is an angle whose vertex is the center of a circle with the two radii lines as its arms, that intersect at two different points on the circle.
The central angle of a circle formula is as follows.
Central Angle = ( s x 360° ) / 2πr
where s is the length of the arc
r is the radius of the circle
Central Angle = 2 x Angle in other segment
Given data ,
Let the radius of the circle be r = 4 units
Let the arc length of the circle be L
Let the central angle be = 270°
So , Central Angle = ( s x 360° ) / 2πr
On simplifying , we get
L = ( 270° / 360° ) x 2πr
L = ( 3/4 ) ( 8π )
L = 18.849 units
Hence , the arc length of the circle is 18.849 units
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Simplify, using the distributive property and then combining like terms.
4m−3(2m+1)
Answer:
4m−3(2m + 1)
= 4m - 3*2m - 3*1
= 4m - 6m - 3
= -2m - 3
Hope this helps!
:)
Answer:
-2m - 3
Step-by-step explanation:
Remember to follow PEMDAS. First, distribute -3 to all terms within the parenthesis:
-3(2m + 1) = (-3 * 2m) + (-3 * 1) = -6m + (-3)
4m - 6m - 3
Simplify. Combine like terms:
(4m - 6m) - 3
(-2m) - 3
-2m - 3 is your answer.
~
What is the surface area of the cube below?
A. 508 units2
B. 512 units2
C. 320 units2
D. 384 units2
Answer:
D
Step-by-step explanation:
because one side surface area is 8x8=64, and there is 6 sides so 64x6 = 384 units2
Answer:
D. 384 units^2
Step-by-step explanation:
The surface area of a cube can be found using the following formula:
S=6s^2
where s is the side length.
In this case, the side length of the cube is 8 units.
s=8 units
Substitute 8 units in for s.
S=6*(8 units)^2
First, evaluate the exponent.
(8 units)^2=8 units * 8 units= 64 units^2
S=6* 64 units^2
Multiply 6 and 64
S=384 units^2
The surface area of the cube is 384 square units, therefore D. 384 units^2 is correct.
Find the slope and y-intercept: (4,2) (8,4)
Answer:
Slope: 1/2
Y-Intercept: 0
Step-by-step explanation:
Use the slope formula and the slope-intercept form to find the slope (m) and y-intercept (b ).
ggefv23ehwdg1uhigvfgwuiderfghvwh4eryu
Answer:
1. 15+63= 78 ft cubed
2. 5.5+33= 38.5 m cubed
Can someone please help me it’s geometry
Answer:
No, the triangles are not congruent.
Step-by-step explanation:
Triangle HOT has AAS, whilst triangle CLD has ASA. Therefore, the triangles are not congruent. There is also no way to prove that HOT and CLD are isoscles triangles, which means we cannot use ASA or AAS.
What is the root of -100 or √−100
Answer:
The root of -100 is 10i
Step-by-step explanation:
Ten I
Employees from A and company B receive annual bonuses. What information would you need to test the claim that the difference in annual bonuses is greater than $100 at the 0.5 level of significance? Write out the hypothesis and explain the testing procedure in details
Answer:
1. The required information are
The average annual bonuses, [tex]\bar {x}_1[/tex] received by employees from company A
The average annual bonuses, [tex]\bar {x}_2[/tex] received by employees from company B
The standard deviation, σ₁, of the average annual bonuses for employees from company A
The standard deviation, σ₂, of the average annual bonuses for employees from company A
The number of employees in company A, n₁
The number of employees in company B, n₂
2. The null hypothesis is H₀: [tex]\bar {x}_1[/tex] - [tex]\bar {x}_2[/tex] ≤ 100
The alternative hypothesis is Hₐ: [tex]\bar {x}_1[/tex] - [tex]\bar {x}_2[/tex] > 100
Step-by-step explanation:
1. The required information are
The average annual bonuses, [tex]\bar {x}_1[/tex] received by employees from company A
The average annual bonuses, [tex]\bar {x}_2[/tex] received by employees from company B
The standard deviation, σ₁, of the average annual bonuses for employees from company A
The standard deviation, σ₂, of the average annual bonuses for employees from company A
The number of employees in company A, n₁
The number of employees in company B, n₂
2. The null hypothesis is H₀: [tex]\bar {x}_1[/tex] - [tex]\bar {x}_2[/tex] ≤ 100
The alternative hypothesis is Hₐ: [tex]\bar {x}_1[/tex] - [tex]\bar {x}_2[/tex] > 100
The z value for the hypothesis testing of the difference between two means is given as follows;
[tex]z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})}{\sqrt{\frac{\sigma_{1}^{2} }{n_{1}}-\frac{\sigma _{2}^{2}}{n_{2}}}}[/tex]
At 0.5 level of significance, the critical [tex]z_\alpha[/tex] = ± 0
The rejection region is z > [tex]z_\alpha[/tex] and z < -[tex]z_\alpha[/tex]
Therefore, the value of z obtained from the relation above more than or less than 0, we reject the null hypothesis, and we fail to reject the alternative hypothesis.
Which triangles are similar? d a b c
Answer:
b and d
Step-by-step explanation:
Solve for w.
–0.05 + 2.3w − 14w = –6.89 − 13.6w
w =
Answer:
w = -3.6
Step-by-step explanation:
→Add like terms (2.3w and -14 w):
-0.05 + 2.3w - 14w = -6.89 - 13.6w
-0.05 -11.7w = -6.89 - 13.6w
→Add 11.7w to both sides:
-0.05 = -6.89 - 1.9w
→Add 6.89 to both sides:
6.84 = -1.9w
→Divide both sides by -1.9:
-3.6 = w
Answer:
[tex] \boxed{w = - 3.6} [/tex]
Step-by-step explanation:
[tex] = > - 0.05 + 2.3w - 14w = - 6.89 - 13.6w \\ \\ = > - 0.05 - 11.7w = - 6.89 - 13.6w \\ \\ = > - 0.05 - 11.7w + 13.6w = - 6.89 \\ \\ = > - 0.05 + 1.9w = - 6.89 \\ \\ = > 1.9w = - 6.89 + 0.05 \\ \\ = > 1.9w = - 6.84 \\ \\ = > w = - \frac{6.84}{1.9} \\ \\ = > w = - 3.6[/tex]
The diagram shows a floor in the shape of a trapezium. Tim is going to paint the floor. Each 5 litre tin of paint costs £16.99 and 1 litre of paint covers an area of 1.9 m2 How much would it cost to buy all the paint he needs? You must show how you get your answer. 0 m 16m £16.99
Answer: £186.89
Step-by-step explanation:
-We are given that each 5l tin of paint costs £16.99 . We therefore divide the paint used by 5 and multiply by £16.99:
Hence, it will cost £186.89 to buy all the paint
Answer:
=£186.89
Step-by-step explanation:
A=1/2(a+b)h
a||b dimensions
A=1/2(16+10)×7.6
=98.8m²
Given that 1 litre of paint covers an area of 1.9 sq m, we divide the area of the trapezium by this and multiply by the price per liter to get total cost:
paint used= Area/paint m²
98.8/1.9
=52 litres
We are given that each 5l tin of paint costs £16.99 . We therefore divide the paint used by 5 and multiply by £16.99
52/2
=10.4
11tins
cost=11×16.99
=£186.89
A 32cm long string just fits round the perimeter of a square board. The area of the board is
Answer:
64cm2
Step-by-step explanation:
(32÷4)=8
8×8=64cm2
Answer:
64cm²
Step-by-step explanation:
perimeter of a square= 4 x side of the square
perimeter= 32cm
i.e side of the square= 32/4
side= 8cm.
Area of square = side of the square ²
=8²
therefore, area of square = 64cm²
find the perimeter of the triangle defined by the coordinates (9,0) , (-5,0) and (-10,6)
Answer:
PERIMETER = 41.73 units
Step-by-step explanation:
To find the perimeter of the triangle, we will follow the steps below:
Let the coordinate of the triangle be ABC, that is
A(9,0) B(-5,0) and C(-10,6)
We will first find distance AB, BC and CA using the distance formula
|D| = √(x₂-x₁)² +(y₂-y₁)²
A(9,0) B(-5,0)
x₁ =9 y₁=0 x₂=-5 y₂=0
substitute the values into the formula
|AB| = √(-5-9)² +(0-0)²
= √(-14)² +(0)²
=√196
=14
|AB| = 14 units
B(-5,0) C(-10,6)
x₁ =-5 y₁=0 x₂=-10 y₂=6
substitute the values into the formula
|BC| = √(-10+ 5)² +(6-0)²
=√(-5)² +(6)²
=√25 + 36
=√61
≈7.81
|BC| ≈7.81 units
C(-10,6) A(9,0)
x₁ =-10 y₁=6 x₂=9 y₂=0
substitute the values into the formula
|CA| = √(9+10)² +(0-6)²
= √(19)² +(-6)²
=√361 +36
=√397
≈19.92 units
|CA|≈19.92 units
Perimeter of triangle = |AB|+|BC|+|CA|
=14+7.81+19.92
=41.73
PERIMETER = 41.73 units
Which pair of polygons are congruent?
A) pairs 1,2,3,and 4
B) pairs 1 and 4
C) pairs 1,2,and 3
D) pairs 2 and 4
Pair 2 shows one figure rotated 180 degrees compared to the other, and translated as well. So they are congruent (ie the same).
Pair 4 shows one triangle reflected over the vertical line x = 22 to get the other triangle; which shows they are the same triangle.
The other pairs are not congruent. You can show that the areas of each figure being different is enough to prove they aren't the same figure.
Solve for r.
–7r = –8r − 20
r =
Answer:
r = -20
Step-by-step explanation:
–7r= –8r−20
Add 8r to both sides
r = -20
Answer:
[tex] \boxed{r = -20} [/tex]
Step-by-step explanation:
[tex] = > - 7r = - 8r - 20 \\ \\ = > - 7r + 8r = - 20 \\ \\ = > 8r - 7r = - 20 \\ \\ = > r = - 20[/tex]
An architect is designing a house. He wants the bedroom to have the dimensions of 8 ft by 4 ft by 7 ft. The architect doubles all three dimensions to create the den. Does that mean the den will have double the volume of the bedroom? First, find the volume of the bedroom. Solve on paper. Then check your work on Zearn. The bedroom will be ft3.
Answer:
No. The den will have 8 times the volume of the bedroom.
Step-by-step explanation:
The architect wants the bedroom to have the dimensions of 8 ft by 4 ft by 7 ft. Let's find the volume of the bedroom:
8 * 4 * 7 = 224 cubic feet
The architect doubles all three dimensions to create the den. This means that the den has dimensions as 16 ft by 8 ft by 14 ft.
The volume of the den is:
16 * 8 * 14 = 1792 cubic feet
Double of 224 cubic feet is 448 cubic feet.
Hence, the den will not have double the volume of the bedroom instead it will have a volume 8 times the that of the bedroom.
Doubling the initial dimensions of 8 ft. by 4 ft. by 7 ft. means that the
volume will 8 times the initial volume or 1,792 ft.
What is the scale factor of volume be used?
The dimensions of the room = 8 ft. by 4 ft. by 7 ft.
The amount by which the architect increases the dimension = Double the dimensions
Solution;
The volume of the room, V = 8 ft. × 4 ft. × 7 ft. = 224 ft.³
When the dimensions are doubled, we have;
Length = 2 × 8 ft. = 16 ft.
Width = 2 × 4 ft. = 8 ft.
Height = 2 × 7 ft. = 14 ft.
The new volume of the bedroom = 16 ft. × 8 ft. × 14 ft. = 1792 ft.³
Therefore;
The volume of the bedroom after doubling the dimension will be 1,792 ft.³Scale factor of volume = (Scale factor of length)³
Therefore;
Doubling the dimensions means that the volume of he room will be
multiplied by 2³ = 8 rather doubling the initial volume.
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Suppose you physically simulate the random process of rolling a single die. (a) After 1010 rolls of the die, you observe a "one" 44 times. What proportion of the rolls resulted in a "one"? (b) After 2020 rolls of the die, you observe a "one" 22 times. What proportion of the rolls resulted in a "one"?
Answer:
(a) 0.4 or 40%
(b) 0.1 or 10%
Step-by-step explanation:
(a) If you get 4 "ones" after 10 rolls of the die, the proportion of the rolls that resulted in "ones" is:
[tex]p=\frac{4}{10}\\ p=0.4[/tex]
(b) If you get 2 "ones" after 20 rolls of the die, the proportion of the rolls that resulted in "ones" is:
[tex]p=\frac{2}{20}\\ p=0.1[/tex]
