Answer:
9.5 x 10^-3
Step-by-step explanation:
Move the decimal place until the leading digit is between 1 and 10, about three places to the right.
The exponent we use to notate our movement is negative, as we moved it to the right, so since we moved it three places to the right, it is -3.
Write it in the notation form m x 10^n, where m is that number between 1 and 10, and n is the exponent.
Your answer is 9.5 x 10^-3
A cone has a height of 6 inches and a diameter of 10 inches. What is its volume?
Use ≈ 3.14 and round your answer to the nearest hundredth
Answer:
V = 157 in³
Step-by-step explanation:
the volume (V) of a cone is calculated as
V = [tex]\frac{1}{3}[/tex] πr²h ( r is the radius and h the height )
here diameter = 10 , then r = 10 ÷ 2 = 5 , then
V = [tex]\frac{1}{3}[/tex] × 3.14 × 5² × 6 ( cancel 3 and 6 by 3 )
= 3.14 × 25 × 2
= 3.14 × 50
= 157 in³
Find the vertex of a parabola with an equation of 3x^2+9x-y-3=0.
Answer:
Step-by-step explanation:
We will have to convert this to vertex form.
First we add y to both sides.
y = 3x^2 + 9x - 3
The vertex form is y = a(x – h)^2 + k
y = 3(x^2 + 3x) - 3
We need to complete the square now, and half if 3 is 1.5, and 1.5^2 is 2.25, so we add 2.25 inside the parentheses but we have to be careful, because if we subtract 2.25 from outside the parentheses it wouldn't work because the 2.25 inside the parentheses is being multiplied by 3, so we have to subtract 2.25*3=6.75 from the outside.
y=3(x^2 + 3x + 2.25) - 9.75
we can simplify this now to
y=3(x + 1.5)^2 - 9.75
and now this is vertex form. From here it is incredibly easy to get the vertex. Just take the x value required to make the total in the parentheses zero, so in this problem it would be -1.5 (Because (-1.5+1.5)^2 is zero) and then you have your x coordinate. From there we just take k, which in this problem is -9.75, and it is the y value of our vertex.
In conclusion, the vertex is (-1.5. -9.75)
Tisha brought chocolate and vanilla cupcakes to school for her birthday. 50 students decided to take a cupcake, and 27 of them picked vanilla. What percentage of the students picked a vanilla cupcake?
Write your answer using a percent sign (%).
Answer:
48% of students picked a vanilla cupcake
Step-by-step explanation:
We can get 48% from this question by turning this data into a fraction
27 students picked vanilla out of a total amount of 50
= 27/50
= 48%
This equals a percentage of 48% of students picking a vanilla cupcake
Answer:
48%
Step-by-step explanation:
5) Jackson bought an ultra-slim Television. The screen measures 13 cm in length and 12 cm in width. Television screen sizes are decided by the length of the diagonal. What is size of this screen? Round your answer to the nearest whole number.
6) A handicap camp ramp is located at the back of the building. The ramp has a 550 incline. The height of the ramp is 15m. How long is the ramp?
HELP PLEASE :?
5. If Jackson bought an ultra-slim Television. The size of this screen is 17.69.
6. If the ramp has a 550 incline and the height of the ramp is 15m. The height of the ramp is -68.24.
How to find the height?5. Size of the screen
Pythagorean theorem
c²= a² + b²
c² = 12² + 13²
c²= 144+169
c = √313
c = 17.69
6. Height
Using SOH CAH TOA
sin550= 15/x
x= 15/sin550
x= 15/-0.2195
x= -68.24
Therefore the size is 17.69 and the height is -68.24.
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The function y = f(x) is graphed below. What is the average rate of change of the function f(x) on the interval 1 < x<1?
The average rate of change of the function is: 0
What is average rate of change?You should know that average rate of change is also referred to as the slope of the function
At point where x = -8, the value of f(-8) = -10 and
At x = -1, the value of f(-1) = -10
We have to determine the average rate of change of the function f(x) on the interval -8 ≤ x ≤ -1.
When x₁ = -8, f(x₁) = f(-8) = -10 also
when x₂ = -1, f(x₂) = f(-1) = -10
This implies that
Average rate = [f(x₂) - f(x₁)] / [ x₂ - x₁]
= [f(-1) - f(-8) ] / [-1-(-8)]
= [-10 - (-10)] / [-1+8]
= [-10 + 10] / 7
= 0 / 7
= 0
In conclusion, 0 is the average rate of change which is also the slope of the function
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Find the slope and y-intercept of the graph of the equation.
y=4 x+8
Select the correct choice and fill in any answer boxes in your choice below.
A. The slope is ____ .
B. The slope is undefined.
The slope of the equation y = 4x + 8 is 4 and the y-intercept is 8.
How to find the slope and y-intercept of an equation?The slope of a line is the change in the dependent variable with respect to the change in the independent variable.
The slope is rise over run.
Therefore, the equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptHence,
y = 4x + 8
Therefore, the slope is 4 and the y-intercept is 8
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There are3 numbers for the combination to the skating rink’s safe. The first number is 19. The other2 numbers can be multiplied together to give a product of 42. What are the possibilities?
Answer: 7 and 6
Step-by-step explanation: 7 x 6 = 42
i rlly need help i don’t get it
The largest possible whole-number length for the third-side is 27 .
What is whole number ?
Whole numbers are made up of all the ordinal numbers and 0. Natural numbers are the names given to counting numbers in mathematics. Thus, the definition of a whole number is a grouping of all natural numbers plus 0. Along with zero, all positive integers are also considered whole numbers.
There are no fractions, decimals, or negative integers in whole numbers, which are actual numbers. There is no fraction or decimal equivalent to zero. It is neutral; neither good nor bad. The whole-number rule is observed by zero.
All natural numbers and 0 are included in the category of whole numbers. They are a subset of real numbers, which exclude negative numbers, decimals, and fractions. Whole numbers include counting numerals as well.
Consider a triangle with side lengths a , b ,c such that a < b < c
a = 18 and b = 10 are the two known sides
Let c be the missing side length
The missing side has the property that...
a - b < c < a + b
18 - 10 < c < 18 + 10
8 < c < 28
Meaning that if c is a whole number then it can take on any of these values { 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 }
So c = 27 is the largest possible third side, where only whole number sides are considered.
We can't have a third side of 28 because the two other sides add to a+b = 10 + 18 = 28 and a triangle wouldn't form (instead only a straight line would).
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An experiment involves selecting a numbered chip, some black and some white, from a bag of chips. The probability of selecting a black chip with an even number is 1/2. The probability of selecting a black chip is 3/5.
What is the probability of selecting a chip with an even number given that the chip is black?
Enter your answer as a simplified fraction.
The probability of selecting a chip with an even number, given that the chip is black, is 1/10.
What is the probability?The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.
Given:
An experiment involves selecting a numbered chip, some black and some white, from a bag of chips.
The probability of selecting a black chip with an even number is 1/2.
Let P(B and E) = 1/2
The probability of selecting a black chip is 3/5.
P(B) = 3/5
The probability of selecting a chip with an even number given that the chip is black
P(W) = 3/5 - 1/2
= 6-5/10
= 1/10
Therefore, the probability is 1/10.
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PLEASE HELP please..
Answer:
49 ft tall
Step-by-step explanation:
Using a ratio
7 is to 3 as height is to 21 ft
7/3 = height / 21
height = 21 * 7/3 = 49 ft tall
If two angles form a linear pair, what else do we know about the angles? List two things that are true about two angles that form a linear pair.
Answer:
When two lines intersect each other at a single point, linear pairs of angles are formed. If the angles so formed are adjacent to each other after the intersection of the two lines, the angles are said to be linear. If two angles form a linear pair, the angles are supplementary, whose measures add up to 180°.
Simplify the expression (h+ k)²-(h - k)².
Hence, by substituting a suitable value of h and
of k, find the value of 165²- 35².
PLEASE HELP please..
Answer:
2nd choice
Step-by-step explanation:
m/54.2 = 82.5/271
Cross multiply:
m(271) = (82.5)(54.2)
m = 4471.5/271 = 16.5
If a^1/2=r then which of the following are true statements
For exponential equation a^1/n = r option D is true i.e. r^n=a.
What are exponential equations?
Exponents are used in exponential equations, as the name implies. We already know that the exponent of a number (base) specifies how many times the number (base) has been multiplied. But what happens if a number is variable? When the power is a variable in an equation, it is referred to as an exponential equation.
For example, 3^x = 81, 5^x - 3 = 625, 62^y - 7 = 121, etc are some examples of exponential equations.
Exponential equations are classified into three categories. These are :
Equations on both sides with the same base. (For instance, 4^x = 4^2)Equations that may be constructed to have the same base. (For example, 4^x = 16 can be represented as 4^x = 4^2.)Equations that cannot be constructed to have the same base. (For instance, 4^x = 15.As given,
a^1/n=r
Now we take 1/n from left side of exponential equation to right side i.e.
a=r^n (As a^1/2 = 4 ---> a=4^2)
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PLEASE HELP
Identify and label the hypotenuse, adjacent and
opposite sides on the given right triangle using
the reference angle.
Solve for the missing side in the given triangle.
Find the sine, cosine, and tangent of the referenced angle.
The missing side in the triangle is 13 units which is the hypotenuse. The values of sine, cosine, and tangent of the referenced angle are 5/13, 12/13, and 5/12 respectively.
What are trigonometric functions?Trigonometry is the branch of mathematics that deals with particular functions of angles and how to apply them in calculations. There are six widely used angles-related trigonometric functions. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant(csc) are their respective names and acronyms.
In the given triangle the reference angle is θ.
So, the adjacent side (P) has a length of 12 units. The opposite (B) is the side having a length of 5 units. So, the hypotenuse will be
Then, acc to Pythagoras theorem, the hypotenuse (H) will be
H² = P² + B²
H² = 5² + 12²
H² = 25 + 144
H² = 169
H = √169
H = 13 units
This is the missing side of the given triangle.
The sine is
sinθ = opposite/ hypotenuse
= 5/13
cosθ = adjacent/ hypotenuse
= 12/13
tanθ = opposite/ adjacent
= 5/12
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Somebody please help me
Answer:
70
Step-by-step explanation:
On Tuesday, the balance in your bank account is $40.
Since from Wednesday to Friday you withdraw $10 a day, keep adding $10 to each day.
On Wednesday the balance is $40 + $10 = $50
On Thursday the balance is $50 + $10 = $60
On Friday the balance is $60 + $10 = $70
The balance in your bank account at the end of the day on Friday is $70
In how many different ways can the ribbons be awarded?
The total number of different ways in which the ribbons can be awarded is 24,024 ways, so the third option is the correct one.
In how many ways can the ribbons be awarded?There is a competition with 14 dogs, and there are 4 prizes for the dogs.
To find the number of ways in which the ribbons (prizes) can be awarded, we need to take the product between the numbers of options for each.
For example for the blue ribbon (first prize) there are 14 dogs to select, so there are 14 options.
For the red one there are 13 options (because one dog is already selected for the blue ribbon).
For the yellow one there are 12 options.
For the white there are 11 options.
Then the total number of different combinations is:
C = 14*13*12*11 = 24,024
Thus, the third option is the correct one.
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how to calculate (1/2)^(4/3)
Answer:0.39685026299
Step-by-step explanation:
...... calculator
what is the result when -7/8 is multiplied by -3.5?
Answer:
Step-by-step explanation:
First, I will convert the decimal as a fraction or decimal, whichever one you prefer. I did fraction. So, -3.5 is the same as -7/2.
Second, for fraction multiplication, you will multiply the numerator and then the denominator.
[tex]\frac{-7 times -7}{8 times 2} = \frac{49}{10}[/tex]
Third, we will convert the improper fraction to a mixed fraction by using long division 49 divided by 16 = 3R1.
3 WILL BE YOUR WHOLE NUMBER. 1 IS YOUR NUMERATOR AND 16 IS YOUR DENOMINATOR.
The Answer is 3 [tex]\frac{1}{16}[/tex]. Letter D
13) x=
14) x=
15) x=
16) x=
17) x=
18) x=
The angle measures of x are given as follows:
13) x = 50º.
14) x = 40º.
15) x = 112º.
16) x = 32º.
17) x = 22º.
18) x = 120º.
How to obtain the angle measures?For item 13, at the triangle at the right, we have that the sum of the measures of the internal angles of a triangle is of 180º, hence:
43 + 57 + y = 180
y = 80º.
Meaning that x is the base angle of an isosceles triangle, for which the top angle is of 80º, hence:
2x + 80 = 180
2x = 100
x = 50º.
For item 14, we have that the third angle in the triangle with angles 50º and 80º is the complement of x, hence:
50 + 80 + 90 - x = 180
x = 40º.
For item 15, the internal angles are given as follows:
2y + 44 = 180
2y = 136
y = 136/2
y = 68.
The external angle is supplementary with it's internal angle, hence:
x = 180 - 68 = 112º.
For item 16, the internal angles of the triangle are given as follows:
90º.x.180 - 122 = 58ºHence:
90 + x + 58 = 180
x = 32º.
For item 17, the internal angles are given as follows:
180 - (6x - 7).2x.103 - x.Hence the value of x is obtained as follows:
180 - (6x - 7) + 2x + 103 - x = 180
-6x + 7 + 2x + 103 - x = 0
5x = 110
x = 22º.
For item 18, we have an equilateral triangle, hence the internal angles are of 60º and the external angles, representing the value of x, are given as follows:
x = 180 - 60 = 120º.
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6) In the following rectangle ABCD, the sum of the lengths of AB, BC, and CD is 90 cm. The
sum of the lengths of BC, CD, and AD is 78 cm. What is the perimeter of rectangle ABCD?
The perimeter of rectangle ABCD will be 112 centimeters.
What is the perimeter of the rectangle?Let W be the rectangle's width and L its length.
The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be
Perimeter of the rectangle = 2(L + W) units
In the following rectangle ABCD, the sum of the lengths of AB, BC, and CD is 90 cm. The sum of the lengths of BC, CD, and AD is 78 cm.
We know that in a rectangle ABCD, AB = CD, and BC = AD. Then we have
AB + BC + CD = 90
2 AB + BC = 90 ...1
BC + CD + DA = 78
2 BC + AB = 78 ...2
From equations 1 and 2, we have
3AB + 3BC = 168
AB + BC = 56
2(AB + BC) = 112 cm
P = 112 cm
The perimeter of rectangle ABCD will be 112 centimeters.
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Solve for k.
-6k-10 = 10 - 10k
Answer: The solution for k is -3/4.
To solve the equation, you can follow these steps:
Add 10k to both sides of the equation: -6k - 10 = 10 - 10k becomes -6k = 20
Divide both sides by -6: -6k/-6 = 20/-6 becomes k = -3/4
Step-by-step explanation:
Write the number that represents the give secasrio. (DOK 1)
6. One-fourth of the students brought their hunch to school.
7. After the penalty, there was a loss of 15 yards on the play.
8. He gained 6 pounds of muscle.
9. He made a 535 deposit into a bank account.
10. The temperature was 9 degrees below zero.
11. Two-thirds of the crewed left the stadium.
12. She received $20 on her birthday.
13. The student lost 10 points on the final exam.
14. He made a 570 withdrawal from a bank account.
15. One-half of the gallon of milk is gone.
Write the number that represents the given scenario. (DOK 1)
11. A submarine is 350 feet below sea level.
12. The family traveled 500 miles south on a road trip.
13. A rabbit hops 10 feet forward.
14. The temperature dropped 13 degrees.
15. A hot air balloon traveled 20 miles north.
The expression of the numbers as negative or positive is as follows;
6. ¹/₄
7. -15 yards
8. +6 pounds
9. +535 pounds
10. -9 degrees.
11. -²/₃ of the crowd
12. +$20
13. -10 points
14. -570
15. - ½
11. -350 feet
12. -500 miles
13. +10 feet
14. -13 degrees
15. + 20 miles
How to express numbers?We can express numbers in this regards as either positive or negative with a positive number indicating a gain while a negative number indicates a loss.
Thus;
6. One-fourth of the students brought their hunch to school is expressed as; ¹/₄
7. After the penalty, there was a loss of 15 yards on the play is expressed as; -15 yards
8. He gained 6 pounds of muscle is expressed as; +6 pounds
9. He made a 535 deposit into a bank account is expressed as; +535 pounds
10. The temperature was 9 degrees below zero is expressed as; -9 degrees.
11. Two-thirds of the crewed left the stadium is expressed as; -²/₃ of the crowd
12. She received $20 on her birthday is a gain and expressed as; +$20
13. The student lost 10 points on the final exam is a loss and expressed as; -10 points
14. He made a 570 withdrawal from a bank account is a loss and is expressed as; -570
15. One-half of the gallon of milk is gone is a loss and is expressed as; - ½
Write the number that represents the given scenario. (DOK 1)
11. A submarine is 350 feet below sea level is negative and is expressed as; -350 feet
12. The family traveled 500 miles south on a road trip is in the negative y-axis and is; -500 miles
13. A rabbit hops 10 feet forward is positive movement and is; +10 feet
14. The temperature dropped 13 degrees is a loss and is expressed as -13 degrees
15. A hot air balloon traveled 20 miles north is in the positive direction and is expressed as; + 20 miles
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A pencil 10 cm long is kept inside a cylindrical glass as shown in figure. If the radius of the base of the glass is 3 cm, find its height.
The length of the cylinder for the condition is 11.66 cm
What is a cylinder?One of the fundamental three-dimensional shapes in geometry is the cylinder, which has two distant, parallel circular bases. At a predetermined distance from the centre, a curved surface connects the two circular bases. The axis of the cylinder is the line segment connecting the centres of two circular bases. The height of the cylinder is defined as the distance between the two circular bases.
Given the height of the pencil = 10 cm
and kept diagonally in cylinder,
and radius of cylinder = 3 cm
the relation between height, radius and diagonal of cylinder is
d² = h² + (2r)²
h² = d² - (2r)²
where d is diagonal and r is radius
h² = 10² + (2 x 3)²
h² = 100 + 36
h² = 136
h = √136
h = 11.66 cm
Hence height of cylinder is 11.66 cm.
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the image of question is attached.
Answer:
Answer:height = √919.539cm
Step-by-step explanation:
we have to find height from slant height
we have to find height from slant heightso the formula is height= v(I²-r²)
we have to find height from slant heightso the formula is height= v(I²-r²)slant height I = 10 cm = 100 cm
we have to find height from slant heightso the formula is height= v(I²-r²)slant height I = 10 cm = 100 cmradius r = 3 cm = 9cm
we have to find height from slant heightso the formula is height= v(I²-r²)slant height I = 10 cm = 100 cmradius r = 3 cm = 9cmheight = √(100-9)
we have to find height from slant heightso the formula is height= v(I²-r²)slant height I = 10 cm = 100 cmradius r = 3 cm = 9cmheight = √(100-9)height = √91
we have to find height from slant heightso the formula is height= v(I²-r²)slant height I = 10 cm = 100 cmradius r = 3 cm = 9cmheight = √(100-9)height = √91height = 9.539 cm
Note
please make me brainalist and keep smiling dude I hope you will be satisfied with my answer :-)
A right circular cylinder with its diameter equal to its height is inscribed in a right circular cone.The cone has diameter 10 and altitude 15, and the axes of the cylinder and the cone coincide. find the volume of the cylinder.
O 30/23
O 30/11
O 15/11
O 17/11
O 3/2
The volume of the cylinder is 169.7. (Option C)
Based on the provided information, let the radius of the cylinder be r and diameter of the cylinder be 2r. The diameter and height of the circular cylinder is the same. When examining the cross section of the cone and cylinder, there are two similar triangles. Hence,
(15 – 2r)/15 = r/5
5(15 – 2r)= 15r
75 – 10r = 15r
r = 3
Volume of the cylinder = πr^2h where r is the radius of the cylinder and h is the height of cylinder. As h = 2r, Hence,
V = πr^2(2r) = (22/7)(3^2)(6) = 169.7
Note: The question is incomplete as the options are incorrect. The correct options are A) 127.5 B) 151.6 C) 169.7 D) 168.5
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Answer the following questions
The answers are given below.
What are trigonometric functions?In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.
Given:
1) 2Sin(9θ).Cos(5θ)=1/2(Sin14θ+Sin4θ)
2) Sin(3θ)Sin(5θ)Cos(3θ)Cos(5θ)=1/2(Sin8θ+Sin2θ)
3)Cos6θ+Cos4θ=2Cos5θCosθ
4)Sin(13θ/2)+Sin9θ=2Sin(11θ/2)Sinθ
5)Cosθ=2√5/5
6)Cos2θ=23/2
7)Tan(π/12)=2-√3
8)Sin(165°)=√6-√2 /4
9)Cos(5π/18)Cos(2π/9)-Sin(5π/18)Sin(2π/9)=Cos(π/2)
=0
Hence, these are the answers .
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Data was collected on the amount of time that a random sample of 8 students spent studying for a test and the grades they earned on the test. A scatter plot and line of fit were created for the data.
scatter plot titled students' data, with points plotted at 1 comma 75, 2 comma 70, 2 comma 80, 2 comma 90, 3 comma 80, 3 comma 100, 4 comma 95, and 4 comma 100, and a line of fit drawn passing through the points 0 comma 60 and 2 comma 80
Determine the equation of the line of fit.
y = 5x + 60
y = 5x + 80
y = 10x + 60
y = 10x + 80
The equation of the line of best fit for this data-set is given as follows:
y = 10x + 60.
How to obtain the equation for the line of best fit?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which the coefficients are given as follows:
m is the slope, representing the rate of change of the output of the function relative to the input.b is the y-intercept, representing the value assumed by the function the input assumes a value of zero.The function goes through point (0,60), hence the intercept b of the line of fit is given as follows:
b = 60.
When x increases by 2, from 0 to 2, y increases by 20, from 60 to 80, hence the slope m is obtained as follows:
m = 20/2 = 10.
Hence the line of fit is given as follows:
y = 10x + 60.
Meaning that the third option is correct.
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Answer:
y = 10x + 60.
Step-by-step explanation:
Write an equation of the line that passes through the given points.
(-3,7) and (4,-7)
The equation is _______. (Type your answer in slope-intercept form.)
Considering the expression of a line, the equation of the line that passes through the points (-3,7) and (4,-7) is y= -2x +1.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope can be calculated using:
m= (y₂ - y₁)÷ (x₂ - x₁)
Substituting the value of the slope m and one of the points in the expression of a line, the value of the ordinate to the origin can be obtained.
Equation in this caseIn this case, being (x₁, y₁)= (-3, 7) and (x₂, y₂)= (4, -7), the slope m can be calculated as:
m= (-7 - 7)÷ (4 - (-3))
m= (-7 - 7)÷ (4 +3)
m= (-14)÷ 7
m= -2
Considering point 1 and the slope m, you obtain:
7= (-2)× (-3) + b
7= 6+b
7 -6= b
1= b
Finally, the equation of the line is y= -2x +1.
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Janelle bought a beach chair on sale at 60% of. The original price was 46.95
Answer:
18.78
Step-by-step explanation:
100_60÷100×46.95=18.78
Why should I use a decimal
Answer:
We use decimals every day while dealing with money, weight, length, etc. Decimal numbers are used in situations where more precision is required than whole numbers can provide. For example, when we calculate our weight on the weighing machine, we do not always find the weight equal to a whole number on the scale.
Step-by-step explanation:
Hope this helps!