Answer:
See below
Step-by-step explanation:
1. Standard notation
4.2 × 10⁻⁴ m
A negative exponent indicates
A number between 0 and 1. That the decimal point is shifted that number of places to the left.4.2 × 10⁻⁴ tells you that the decimal number is 4.2, with the decimal point moved four places to the left.
The number becomes 0.000 42 .
2. Metres to millimetres
[tex]4.2 \times 10^{-4}\text{ m} \times \dfrac{10^{3}\text{ mm}}{\text{1 m}} = 4.2\times 10^{-1}\text{ mm = 0.42 mm}}[/tex]
3. Measurements agree?
Yes, because both measurements are the same as 0.42 m.
4. More appropriate measurement
Most measurements should be expressed as a number between 0.1 and 1000, because most people aren’t particularly good at visualizing larger or smaller numbers.
Justin's measurement of 0.42 mm is more appropriate than Amanda's measurement of 4.2 × 10⁻⁴ m.
the polynomial ky^3+3y^2-3 and 2y^3-5y+k when divided by (y-5) leave the same remainder in each case. Find the value of k.
Answer:
[tex]k=\frac{153}{124}[/tex]
Step-by-step explanation:
According to the Remainder Theorem; when P(y) is divided by y-a, the remainder is p(a).
The first polynomial is :
[tex]p(y)=ky^3+3y^2-3[/tex]
When p(y) is divided by y-5, the remainder is
[tex]p(5)=k(5)^3+3(5)^2-3[/tex]
[tex]p(5)=125k+75-3[/tex]
[tex]p(5)=125k+72[/tex]
When the second polynomial:
[tex]m(y)= 2y^3-5y+k[/tex] is divided by y-5.
The remainder is;
[tex]m(5)= 2(5)^3-5(5)+k[/tex]
[tex]m(5)= 225+k[/tex]
The two remainders are equal;
[tex]\implies 125k+72=225+k[/tex]
[tex]\implies 125k-k=225-72[/tex]
[tex]\implies 124k=153[/tex]
[tex]k=\frac{153}{124}[/tex]
A right come has a slant height of 17 feet, and the diameter of the base is 16 feet. What is the height, h, of the cone?
Answer:
h = 15 feet
Step-by-step explanation:
A right triangle is formed by the slant height, the radius of the base and h, with the slant height being the hypotenuse.
Using Pythagoras' theorem in the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
Since base diameter = 16 then radius = 8
h² + 8² = 17²
h² + 64 = 289 ( subtract 64 from both sides )
h² = 225 ( take the square root of both sides )
h = [tex]\sqrt{225}[/tex] = 15
The height of the given cone will be 15 feet.
What is the Pythagorean theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. The theorem can be used to determine how steep mountains or slopes are. To calculate the distance between an observer and a location on the ground when the observer is looking down from a tower or structure. It is mostly utilized in the construction industry.
Given, A right cone has a slant height of 17 feet, and the diameter of the base is 16 feet.
Since slant height and radius of the base makes a right-angle triangle with the base of radius and hypotenuse of the slant.
Thus, from the Pythagorean theorem:
hypotenuse² = height² + base²
In our case,
Hypotenuse = slant height = 17 feet
Base = radius of base of the cone = 16/2 = 8
Thus,
17² = height² + 8²
height² = 17² - 8²
height² = 225
height = 15 feet
Therefore, the height of the given cone will be 15 feet.
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Tony created a square-shaped poster. The length of each side was 1 1/2 feet. What is the area of the poster? 3ft2 or 2 1/4 ft2??
The answer is 2 1/4 feet.
Multiply:
1 1/2 x 1 1/2
3/2 x 3/2
9/4
2 1/4
Hope this helps!
The number of paper clips that Crystal has is 42 divided by the number of paper clips that Gayle has. If
Gayle has 11 more paper clips than Crystal does, how many paper clips does each have?
Answer:
The number of paper clips that Crystal has is 3 and the number of paper clips that Gayle has is 14
Step-by-step explanation:
Let
x----> the number of paper clips that Crystal has
y ---> the number of paper clips that Gayle has
we know that
[tex]y=x+11[/tex] ----> equation A
[tex]x=42/y[/tex] ----> equation B
substitute equation A in equation B
[tex]x=\frac{42}{x+11} \\ \\x^{2} +11x=42\\ \\x^{2} +11x-42=0[/tex]
Solve the quadratic equation by graphing
The solution is [tex]x=3\ paper\ clips[/tex]
see the attached figure
Find the value of y
[tex]y=3+11=14\ paper\ clips[/tex]
therefore
The number of paper clips that Crystal has is 3
The number of paper clips that Gayle has is 14
Systematic random sampling is used to interveiw residents in 25% of 80 apartments in a building. The sampling interval would be
A.) 4
B.)20
C.)5
D.)16
The answer is A, A is the answer
The sampling interval would be 20, the correct option is B.
What is a Random Sampling?It is a type of sampling technique in which each sample has an equal probability of being chosen.
The total number of residents in the building is 80.
Random sampling is done and the residents are interviewed.
The percentage of the residents that are being interviewed is 25%.
The sampling interval has to be calculated.
The sampling interval is given by = 25 % of 80
= 25 * 80 / 100
= 20
The number of residents that were interviewed is 20.
The sampling interval is 20 people.
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Find the volume of the toy rocket shown. The rocket consists of a prism and a pyramid
Answer: [tex]8.66in^3[/tex]
Step-by-step explanation:
The oy rocket shown is formed by a rectangular prism and a regular pyramid whose base is a square.
The volume of the rectangular prism can be calculated with:
[tex]V_{rp}=l*w*h[/tex]
Where "l" is the length, "w" is the width and "h" is the height.
You can observe that:
[tex]l=8in\\w=1in\\h=1in[/tex]
Then, you can substitute values:
[tex]V_{rp}=(8in)(1in)(1in)=8in^3[/tex]
The volume of the regular square pyramid can be calculated with:
[tex]V_p=\frac{s^2*h}{3}[/tex]
Where "s" is the lenght of a side of the base and "h" is the height of the pyramid.
You can observe in the figure that:
[tex]s=1in\\h=2in[/tex]
Substitute into the formula. Then:
[tex]V_p=\frac{(1in)^2(2in)}{3}=\frac{2}{3}in^3[/tex]
The volume of the toy rocket is the sum of the volume of the rectangular prism and the volume of the regular square pyramid. Then:
[tex]V_{toy}=8in^3+\frac{2}{3}in^3=8.66in^3[/tex]
What is the value of x?
Answer:
15
Step-by-step explanation:
The angle in total is 90* because its a right angle.
The equation is 4x+30=90
subtract 30 from both sides
4x=60
divide 4 from both sides
x=15
hope this helped!
Answer:
15
Step-by-step explanation: 90-30=60 60÷4=15
Select ALL the correct answers.
Select all of the equations with a solution of x = 3.
Answer:
A.
C.
D.
Step-by-step explanation:
Answer:
the first, third, and the 4th
Step-by-step explanation:
Find the volume of the prism.
Answer: 120 units3
Explanation: When finding the base of a prism, you must always multiply the side with the right angle. So basically, 5 is ignored because it does not have a right angle.
1st step: 3*4=12
2nd step: 12/2=6 (because the tringle which is the base is half a square)
3rd step: 6*20=120
The ending is unit 3 because it is volume. Area is unit 2 and we don't know if the prism is in cm so it is not A, or B, and D is the incorrect answer.
In conclusion:
120 units 3
Hope this helped!
Alin
this system of equation (d=5t+2
2d=4+10t) have infinitely many solutions. which of the following statements is NOT true?
a. the graphs of the equations are parallel lines
b. the equations are equivalent
c.every solution to the first equation is a solution to the 2nd equation
d.the graph of the solution to the system is a straight line.
The answer is a. If the graphs of the equations were parallel lines then they would have no solutions.
Hope this helps!
If this helps you please make it brainliest.
The statement is NOT true will the graphs of the equations are parallel lines because the system has no solution. Then the correct option is A.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
If the slopes are different then the system has one solution.If the slopes are equal but have different intercepts then the system has no solution.If the slopes and intercepts are equal then the system has infinitely many solutions.This system of equations d = 5t + 2 and 2d = 4 + 10t has infinitely many solutions.
The statement is NOT true will the graphs of the equations are parallel lines because the system has no solution. Then the correct option is A.
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what does the electronic fund transfer act do?
Answer: The Electronic Funds Transfer Act is a federal law that protects consumers engaged in the transfer of funds through electronic methods. This includes the use of debit cards, automated teller machines and automatic withdrawals from a bank account.
Step-by-step explanation:
Answer: It limits liability if their debit card is stolen and used
Fill in the blank: in e^3=____
[tex]\(e^3\)=2.71828[/tex]
In [tex]\(e^3\)[/tex], "e" represents Euler's number, an irrational mathematical constant approximately equal to 2.71828. When raised to the power of 3, [tex]\(e^3\)[/tex] signifies the exponential growth of "e" compounded three times. This can be interpreted as the result of continuously compounding interest or growth at a rate of "e" over three time periods. The expression [tex]\(e^3\)[/tex] calculates the value after three such compounding intervals, showcasing the inherent rapid and self-reinforcing nature of exponential growth. In practical terms, [tex]\(e^3\)[/tex] can represent scenarios where a quantity increases or decreases exponentially, such as population growth, financial investments, or decay processes. Understanding [tex]\(e^3\)[/tex] involves recognizing the profound impact of continuous compounding, making it a fundamental concept in various scientific and mathematical applications.
Can someone convert this from hexadecimal??? 8425095
Answer:
[tex]\large\boxed{8425095_{10}=808E87_{16}}[/tex]
Step-by-step explanation:
You divide the given number by 16. Write the result underneath, and the rest of the division on the right.
The number in the hexadecimal system is wrote from the bottom.
10 = A, 11 = B, 12 = C, 13 = D, 14 = E, 15 = F
[tex]\begin{array}{c|c}8425095&7\\526568&8\\32910&14=E\\2056&8\\128&0\\8&8\\0\end{array}\\\\8425095_{10}=808E87_{16}[/tex]
I minimized the steps in the second part. Hope you understand
which of the following represents the graph of f(x)=1/2^x+2
Answer:
Hi! Next time attach all possible answers in media form. Check attachment for the answer. Please mark brainliest I'm trying to get to next rank, have a good day. Message me if you ever need more help.
There are 10 dogs at the dog park on a busy Saturday. 2 of them are pugs.
What is the probability that a randomly selected dog is a pug?
Simplify your answer and write it as a fraction or whole number.
P(pug) =
Answer:
1/5
Step-by-step explanation:
2/10 chance that a pug would be selected
2/10 is simplified to 1/5
The probability that a randomly selected dog is a pug is 1/5.
What is a Probability?It is a ratio of number of required outcomes to the total outcomes.It is usually used to predict the outcome of any event.It is very useful in solving mathematical problems.Given:
There are 10 dogs at the dog park.
2 dogs are pugs.
We have to find the probability that a randomly selected dog is a pug.
We know, probability is given by:
⇒ Probability = Total number of dogs which are pug / Total number of dogs at the park
⇒ Total number of dogs which are pug = 2
⇒ Total number of dogs at the park = 10
⇒ P(pug) = 2/10
⇒ P(pug) = 1/5
Therefore, the probability that a randomly selected dog is a pug is 1/5.
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Since opening night, attendance at play A has increased steadily, while attendance at play B first rose and then fell. Equations modeling the daily attendance y at each play are shown below, Where x is the number of days since opening night. On what day(s) was the attendance the same at both plays? What was the attendance? Play A: y=15x+76 play B: y=-x^2+36x-4
Answer:
(5,151) and (16,316) are days with equal attendance for both plays.
Step-by-step explanation:
https://brainly.com/question/8102047
The correct answer is 5,101
What is the slope of the line that passes through the pair of points (3,-4) and (5,-7).
A. 2/3
B. -2/3
C.-3/2
D. 3/2
The correct answer is C. -3/2
What integer increased by - 12 is 28?
Answer:
40
Step-by-step explanation:
Let n represent the integer. Then the increase can be written as ...
n + (-12) = 28
We can add 12 to both sides of this equation:
n + (-12) + (+12) = 28 +12
n + 0 = 40 . . . . . . -12 and 12 total to zero; 28 and 12 total to 40.
n = 40
The integer is 40.
PLEASEEEE answer!!!! NEED THIS TO GRADUATE
Answer:
number of students with blue eyes and blond hair= 42
Number of students with grey eyes and brown hair= 5
Difference of number of kids with grey eyes and brown hair and the number of students with green eyes and black hair =6
Difference of the number of students with green eyes and blond hair and the number of students with grey eyes= 14
there are 858 calories 13 serving of cereal. if a bowl holds 2 servings, how many calories are in the bowl?
Answer:
132
Step-by-step explanation:
858/13=66
66*2=132
(17 Leon uses 3/4 cup water to make a serving of iced tea.
Part A
If Leon makes 17 servings of iced tea, how many cups of water does
he use?
-cups
Part B
If the water cooler holds 88 servings of iced tea, how many cups of tea
does the cooler have?
cups
Answer:
A.) 12 3/4 cups
B.) 117 1/3
Step-by-step explanation:
Part A
If one serving of ice tea contains 3/4 cup of water, how much does 7 serving have?
To answer this, you must multiply 3/4 and 17
17 is the same as 17/1, so multiply the numerators and denominators
17 x 3 = 51
1 x 4 = 4
51/4 = 12 3/4
So, Leon used 51/4 or 12 3/4 cups of water
Part B
If the cooler has 88 servings of tea, how many cups of water does it have?
To solve this, divide 88 by 3/4
Dividing 88 by 3/4 is the same as multiplying 88 by 4/3.
Again, 88 is the same as 88/1 so multiply the numerators and the denominators.
88 x 4 = 352
1 x 3 = 3
352/3 = 117 1/3
So, there are 352/3 or 117 1/3 cups of water in the cooler
I hope this helps!
To make 17 servings of iced tea, Leon uses 12.75 cups of water. If the water cooler holds 88 servings of iced tea, it contains 66 cups of water.
The student is asking how to calculate the total amount of water needed for 17 servings of iced tea, with each serving using 3/4 cup of water. To find the total, we multiply the number of servings by the amount of water per serving:
17 servings times 3/4 cup/serving = 12.75 cups
For part B, to find out how many cups are in 88 servings:
88 servings times 3/4 cup/serving = 66 cups
A gym container holds 50 balls of two sizes and two colors. Twenty-two balls are large and red, 12 balls
are small, and 25 balls are green. How many of the balls are small and green.
Since only 12 balls are small, each color has 25, 22 red balls are large - that leaves 3 red balls that are small. 12 small balls total less the 3 red small balls - that leaves 9 green small balls.
what mixed number is equivalent to 19/6
Answer:
[tex]3 ^{1}/_{6}[/tex]
Step-by-step explanation:
6 goes into 19 3 times with a remainder of 1.
So your base number is going to be 3 with your remainder of 1 going into your numerator over the denominator of six.
ANSWER
[tex]3 \frac{1}{6} [/tex]
EXPLANATION
The given expression is :
[tex] \frac{19}{6} [/tex]
This is an improper fraction because the numerator is greater than the denominator.
To express this as a mixed number find the number of times the denominator will divide the numerator exactly and express the remainder over the denominator in simplest form.
[tex] \frac{19}{6} = 3 \frac{1}{6} [/tex]
PLS HELP ASAP!!!! BRAINLIEST AND 20 POINTS!
Aisha can use the expression 120 divided by 10 to determine the solution to which problem?
A.What is 10% of 120?
B.What is 10% of 12?
C.What is 25% of 120?
D.What is 25% of 12?
Answer:
The answer would be A.
Step-by-step explanation:
This is because when you divde 120 by 10, you will be given an answer of 12. This shows that 10% of 120 is 12.
Answer:
A. What is 10% of 120?
Step-by-step explanation:
did it on edge and the other person is correct :] Hope this helps
Ian invested $1,315 in a savings account which earns 2.86% interest compounded quarterly. What will the account be worth in nine years
Answer:
In 9 years, the account will be worth $1699.48
Step-by-step explanation:
Compound interest is interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan. Ian invested $1.315 in savings account which earns 2.86% interest compunded quaterly.
The ammount of money the account will be worth is given by the formula:
[tex]A = P(1 + \frac{[\frac{r}{4}}{100} )^4n[/tex]
where r: Rate of annual interest = 2.86%
n: the number of years = 9
P= Principal ammount = $1315
Then A= $1699.48
on the design of the new car the steering wheel has a diameter with endpoints at (4 9) and (12,3) what are the center and raduis of the wheel
Answer:
The center of the circle is point (8 , 6)
Step-by-step explanation:
* At first lets revise how to find the mid-point between two points
- If (x1 , y1) and (x2 , y2) are the end point of a segment
- If (x , y) is the mid-point of this segment
- To find x add x1 and x2, then divide the answer by 2
∴ x = (x1 + x2)/2
- Similar to find y add y1 and y2, then divide the answer by 2
∴ y = (y1 + y2)/2
∴ The mid-point (x , y) = [(x1 + x2)/2 , (y1 + y2)/2]
* Now lets solve the problem
- The center of the circle is the mid-point of the diameter
- Consider the center of the circle is (x , y)
- (x , y) is the mid-point of the diameter of the circle with endpoints
(4 , 9) and (12 , 3)
- Let (4 , 9) is (x1 , y1) and (12 , 3) is (x2 , y2)
∵ x1 = 4
∵ x2 = 12
∵ x = (x1 + x2)/2
∴ x = (4 + 12)/2 = 16/2 = 8
* Similar
∵ y1 = 9
∵ y2 = 3
∵ y = (y1 + y2)/2
∴ y = (9 + 3)/2 = 12/2 = 6
∴ (x , y) = (8 , 6)
* The center of the circle is point (8 , 6)
Answer:
The center is (8,6) and radius is 5 units of the wheel
Step-by-step explanation:
On the design of the new car the steering wheel has a diameter with endpoints at (4 9) and (12,3)
End point of diameter is (4 9) and (12,3)
As we know mid point of diameter is center of circle.
Mid point formula:
[tex](x,y)\rightarrow (\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})[/tex]
Mid point of (4 9) and (12,3)
[tex]Centre: (\dfrac{4+12}{2},\dfrac{9+3}{2}[/tex]
Center: (8,6)
Radius is distance between center and any one end point of diameter.
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
[tex]R=\sqrt{(8-4)^2+(6-9)^2[/tex]
[tex]R=\sqrt{16+9}=\sqrt{25}[/tex]
Radius = 5
Hence, The center is (8,6) and radius is 5 units of the wheel
how to find the volume
Answer: 226200 ft
Step-by-step explanation:
Length=100 ft
Width=58 ft
Height=78 ft
(78x58x100)/2=226200 ft
I know it sounds crazy, but I'm pretty sure that's the answer.
Answer:
[tex]\large\boxed{V=226,200\ ft^3}[/tex]
Step-by-step explanation:
The formula of a volume of a prism:
[tex]V=BH[/tex]
B - area of a base
H - height
We have the triangle in the Base. The fomula of an area of a triangle:
[tex]A_\triangle=\dfrac{bh}{2}[/tex]
b - base
h - height
We have b = 58ft and h = 78ft. Substitute:
[tex]B=\dfrac{(58)(78)}{2}=(29)(78)=2,262\ ft^2[/tex]
The volume:
B = 2,262 ft², H = 100 ft. Substitute:
[tex]V=(2,262)(100)=226,200\ ft^3[/tex]
please help ASAP! will give brainlist.
What is the value of X line A is parallel to line B and is cut by a transversal?
A. X = 35.
B. X cannot be determined from the information given.
C. X = 19.
D. X = 27.25.
I would personally choose B.
the hypotenuse of a right triangle is 6 more than the shorter leg. the longer leg is three more than the shorter leg. find the length of the shorter leg
Answer:
9
Step-by-step explanation:
shorter leg = x
longer leg = x + 3
Hypotenuse = x + 6
x² + (x + 3)² = (x + 6)²
x² + x² + 6x + 9 = x² + 12x + 36
2x² + 6x + 9 = x² + 12x + 36
x² - 6x - 27 = 0
(x - 9) ( x + 3) = 0
x = 9 or x = -3 (rejected)
The length of the shorter leg of the right angles triangle is 9.
What is a right-angle triangle?
A triangle is said to be right-angled if one of its inner angles is 90 degrees, or if any one of its angles is a right angle. The right triangle or 90-degree triangle is another name for this triangle.
A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse
The right triangle's three sides are interconnected. The Pythagorean Theorem explains this connection. This theorem states that in a right triangle, [tex]h^{2} = x^{2} + y^{2}[/tex];
where, h = hypotenuse; x = perpendicular side; y = base side;
Given that:
shorter leg = x
longer leg = x + 3
Hypotenuse = x + 6
⇒x² + (x + 3)² = (x + 6)²
⇒x² + x² + 6x + 9 = x² + 12x + 36
⇒2x² + 6x + 9 = x² + 12x + 36
⇒x² - 6x - 27 = 0
⇒(x - 9) ( x + 3) = 0
⇒x = 9 or x = -3.
x=-3 is not possible;
Hence, The length of the shorter leg = 9.
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A car rental company charges an initial fee plus a constant fee per kilometer driven.
The table compares the total distance driven on the trip (in kilometers) and the price of the rental (in dollars).
What is the cost of each kilometer driven?
Answer:
The cost of each kilometer driven is $0.6
Step-by-step explanation:
Let
x ------> the total distance driven on the trip (in kilometers)
y -----> the price of the rental (in dollars)
we have
(110,186) and (170,222) ----> see the table
step 1
Find the slope of the linear function
m=(222-186)/(170-110)
m=36/60
m=0.6 $/km
The slope of the linear equation is equal to the unit rate
so
The cost of each kilometer driven is $0.6
Answer:$120
Step-by-step explanation: