Answer:
B
Step-by-step explanation:
[tex]\frac{3.683 \times 10^4}{7.51 \times 10^{12}} \\=\frac{36.83 \times 10^3}{7.51 \times 10^{12}} \\=\frac{36.83}{7.51} \times 10^{3-12}\\ \approx 4.9041 \times 10^{-9}[/tex]
The quotient in the scientific notation form will be 4.9041 × 10⁻⁹. The correct option is B.
What is a scientific notation?Scientific notation can be used to indicate numbers that are either too big or too little to be conveniently stated in decimal form. It may be called scientific form.
Standard notation is the practice of writing a number using nothing but its digits. This is how numbers are usually expressed because traditional number notation does not utilize words.
Given that the two numbers are (3.683 × 10⁴) and (7.51 × 10¹²). The quotient will be calculated as:-
Quotient = (3.683 × 10⁴) ÷ (7.51 × 10¹²)
Quotient = 0.49 x 10⁻⁸
Quotient = 4.9 x 10⁻⁹
The quotient will be 4.9041 × 10⁻⁹.
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What is the square root of negative 64?
Answer: 8 i
Step-by-step explanation: The square root of negative 64 is 8 i. Whenever you are finding a negative square root you need to find what times what will equal that number. 8 x 8 = 64. So the square root is 8. But, since we are finding a negative square root, the answer will be 8 i. i states that 8 is the negative square root of 64.
So the answer is 8 i.
Always add i after the number when finding negative square roots.
NEED IT QUICK! THANK YOU At the start of an experiment, the temperature of a solution was Negative 12 degrees Celsius. During the experiment, the temperature of the solution rose 5 degrees Celsius each hour for 4 hours. Then the temperature changed by Negative 3 degrees Celsius and remained steady. What was the final temperature of the solution?
Negative 11 degrees Celsius
5 degrees Celsius
Negative 5 degrees Celsius
11 degrees Celsius
Answer:
5 degrees Celsius
Step-by-step explanation:
initial temperature = -12°C
temperature after 4 hours = -12°C + 4(5°C)
= -12°C + 20°C
= 8°C
final temperature = 8°C - 3°C
=5°C
Answer:
5 degrees celsius
Step-by-step explanation:
C
write 7/128 as a percentage
Answer:
0.0546875 or if we are rounding 5.47%
Step-by-step explanation:
Answer:
5.46875%
Step-by-step explanation:
To answer this, we need to find 7 divided by 128. Using a calculator, we find that it is 0.0546875. To convert a decimal to a percentage, multiply the number by 100 and put a percent sign next to it. We get 5.46875%.
Three fair coins are flipped. What is the probability that at least 2 of them come up heads?
Answer:
The probability that atleast 2 of them come up heads is 0.5∴ P(A)=0.5Step-by-step explanation:
Given that three fair coins are flipped.
To find the probability that at least 2 of them come up heads:Sample space for the given event is
[tex]S={\{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}\}[/tex]
∴ n(S)=8Let A be the events of getting atleast 2 Heads and is given by
A = {HHH, HHT, HTH, THH}
∴ n(A)=4Probability of Getting atleast 2 Heads in 3 Coin Tosses is
[tex]P(A)=\frac{n(A)}{n(S)}[/tex]
[tex]P(A)=\frac{4}{8}[/tex]
[tex]=0.5[/tex]
∴ P(A)=0.5∴ the probability that atleast 2 of them come up heads is 0.5Ryan is using tiles in his bathroom. He chooses 1" x 2" tiles for the border and would like tiles that are similar to the border as the interior tiles. Interior tiles will be larger by scale factor of 3.5. What are the dimensions of the interior tiles?
Answer:
The area of the interior tiles must be 7 inches ² with dimensions 1.871" x 3.742".
Step-by-step explanation:
Since the interior tiles must be 3.5 larger then the border tiles to calculate the dimensions of the interior tiles we first need to find the area of the border tiles. This is shown bellow:
area border = 1*2 = 2 inches²
The area of the interior tiles is 3.5 larger than that, so we have:
area interior = 2*(area border) = 2*3.5 = 7 inches²
In order to maintain the same proportions as the border tiles we must find a width that is two times the height, so we have:
area interior = width*height = 2*height*height = 2*height²
7 = 2*height²
height² = 3.5
height = sqrt(3.5) = 1.871
width = 2*height = 2*1.871 = 3.74166
The area of the interior tiles must be 7 inches ² with dimensions 1.871" x 3.742".
The interior tiles that Ryan wants to use in his bathroom will have dimensions of 3.5 inches by 7 inches.
Ryan is using 1" x 2" tiles for the border of his bathroom and wants to use similar tiles for the interior that are larger by a scale factor of 3.5.
To calculate the dimensions of the interior tiles, you simply multiply the dimensions of the border tiles by the scale factor. Therefore, the dimensions of each interior tile will be:
2 inches (width of border tile) x 3.5 = 7 inches (width of interior tile)
Find the perimeter of the rectangle. The drawing is not to scale.
29 ft
66 ft
Answer: 190
Step-by-step explanation: The perimeter is the measurement of every side. So multiply 29 by 2 To get 58 since there is two sides with that length. You'd then multiply 66 by 2 to get 132 For the same reason, and then finally add both of those together to get 190
How many solutions are there for quadratic graphed below:
Group of answer choices
1 solution
Infinite Solutions
No solutions
2 solutions
Answer:
No solutions
Step-by-step explanation:
The graph does not contact the x axis
There are no real answers for this reason.
HELP ME PLEASE
Match each transformation or sequence of transformations to an equivalent transformation or sequence of transformations.
a 90° counterclockwise rotation about the origin
a 180° rotation about the origin
a 90° clockwise rotation about the origin
a 90° counterclockwise rotation about
the origin and then a 180° rotation
about the origin
arrowRight
a reflection across the x-axis and then a
reflection across the y-axis
arrowRight
a 90° clockwise rotation about the origin
and then a rotation 180° about the origin
arrowRight
A 90° counterclockwise rotation is the same as a 270° clockwise rotation. A 180° rotation is the same as a reflection across both axes. A 90° clockwise rotation is the same as a 270° counter-clockwise rotation. Two separate rotations of 90° counter-clockwise and then 180° are the same as rotations of 90° clockwise and then 180°.
Explanation:In mathematics, especially in geometry, transformations involve changing the position, size or shape of a figure. The question is about matching specific transformations or sequence of transformations to its equivalent transformation.
A 90° counterclockwise rotation about the origin is equivalent to a 270° clockwise rotation about the origin because they both result in the same final position.A 180° rotation about the origin is equivalent to a reflection across the x-axis and then a reflection across the y-axis. Both of these transformations result in the figure being flipped over the origin.A 90° clockwise rotation about the origin is equivalent to a 270° counterclockwise rotation about the origin as they both result in the same final position.A 90° counterclockwise rotation about the origin and then a 180° rotation about the origin is equivalent to a 90° clockwise rotation about the origin and then a rotation 180° about the origin because they both result in the same final position.Learn more about Geometry Transformations here:https://brainly.com/question/30165576
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Pls help! I need to know if this is right! 50 points!
A small delivery company can deliver only in a small part of the city. Write an equation for the boundary where the company delivers. and find its radius.
Select the appropriate response:
A) (x+1)2+(y-1)2= 25 radius = 5 miles
B) (x-1)2+(y+1)2= 25 radius = 5 miles
C) (x+1)2+(y-1)2= 25 radius = 10 miles
D) (x-1)2+(y+1)2= 25 radius = 10 miles
Answer: B) (x-1)2+(y+1)2= 25 radius = 5 miles
Step-by-step explanation:
In order to get this answer you see that you are adding a negative to x in the first part then multiplying it by 2. Second, you add y+1 then multiplying it by 2. You get the radius of 25 which equals 5 miles. Look at the graph to also check your answers to the problem.
Answer:
B) (x-1)2+(y+1)2= 25 radius = 5 miles
Step-by-step explanation:
Equation of a circle:
(x - h)² + (y - k)² = r²
(h,k) = (1, -1)
r = 5
(x - 1)² + (y - -1)² = 5²
(x - 1)² + (y + 1)² = 25
A video company randomly selected 100 of its subscribers and asked them how many hours of shows they watch per week. Of those surveyed, 45 watch more than 10 hours per week. Based on the data, if the company has 2500 subscribers, how many watch more than 10 hours per week?
Answer:
1,135 people
For every 100 people only 45 people watch more than 10 hours per week. So, the ratio is (45/100), since the company has 2500 we want to know what (x/2500) is. The total ratio becomes (1,135/2,500).
The number is found by dividing 2500 by 100 to receive the common factor of 25. You multiply 45 by 25 to receive your total answer.
Step-by-step explanation:
For every 100 people only 45 people watch more than 10 hours per week. So, the ratio is (45/100), since the company has 2500 we want to know what (x/2500) is. The total ratio becomes (1,135/2,500).
The number is found by dividing 2500 by 100 to receive the common factor of 25. You multiply 45 by 25 to receive your total answer.
Please Help! Determine the number of solutions to each system of equations.
The solution is
The equations with one solution is
y = 0.5x - 2 ; y = -0.5x + 4
y = 2x + 1 ; y = 4x + 1
The equations with no solution is
y = 0.5x + 5 ; y = 0.5x + 1
y = -x - 3 ; y = -x + 3
The equations with infinite number of solutions is
y = 3x + 2.5 ; y = 3x + 2.5
y = -x - 2 ; y = -x - 2
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
a)
y = 0.5x - 2 be equation (1)
y = -0.5x + 4 be equation (2)
On simplifying both the equations , we get
0.5x - 2 = -0.5x + 4
Adding 0.5x on both sides of the equation , we get
x - 2 = 4
Adding 2 on both sides of the equation , we get
x = 6
Substitute the value of x in equation (1) , we get
y = 1
The value of x is 6 and value of y is 1
b)
y = 0.5x + 5 be equation (1)
y = 0.5x + 1 be equation (2)
On simplifying both the equations , we get
0.5x + 5 = 0.5x + 1
Now , the equations are contradictory and there are no solution
c)
y = 2x + 1 be equation (1)
y = 4x + 1 be equation (2)
On simplifying both the equations , we get
2x + 1 = 4x + 1
Subtracting 2x on both sides of the equation , we get
2x + 1 = 1
Subtracting 1 on both sides of the equation , we get
2x = 0
x = 0
Substitute the value of x in equation (1) , we get
y = 1
Therefore , the value of x is 0 and value of y is 1
d)
y = 3x + 2.5 be equation (1)
y = 3x + 2.5 be equation (2)
On simplifying both the equations , we get
3x + 2.5 = 3x + 2.5
Therefore , the equations are similar and there are infinite number of solutions
e)
y = -x - 3 be equation (1)
y = -x + 3 be equation (2)
On simplifying both the equations , we get
-x - 3 = -x + 3
Now , the equations are contradictory and there are no solution
f)
y = -x - 2 be equation (1)
y = -x - 2 be equation (2)
On simplifying both the equations , we get
-x - 2 = -x - 2
Therefore , the equations are similar and there are infinite number of solutions
Hence , the system of equations are solved
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A set of data with 100 observations has a mean of 267. There are six outliners in the data set, which have a mean of 688 if the six outliners are removed, what is the mean of the new data set?
Answer:
272.04
Step-by-step explanation:
We must make a weighted average, as follows:
Each mean will have its weight, which would be the number of observations, therefore, the initial mean has a weight of 100.
And the final mean that we do not know its value but if its 94 (100 - 6) and the other mean that it is 688 and its weight is 6, we have the following equality:
100 * 297 = 688 * 6 + 94 * x
x would be the final mean, solving:
x = (29700 - 4128) / 94
x = 272.04
average after removing those 6 is 272.04
Which expressions represent the product of exactly two factors? Choose 2 answers: Choose 2 answers: (Choice A) A x+yx+yx, plus, y (Choice B) B 5(x+y)5(x+y)5, left parenthesis, x, plus, y, right parenthesis (Choice C) C (x+y)left parenthesis, x, minus, y, right parenthesis, left parenthesis, x, plus, y, right parenthesis (Choice D) D xy, y, z
Answer: B and C because I got it correct so trust me
Step-by-step explanation:
Ez
Samuel and Jason sell cans to a recycling center that pays $0.40 per pound of cans. The table shows the number of pounds of cans that they sold for several days.
Day Samuel's cans(lb) Jason's cans(lb)
Monday 17.4 10.4
Tuesday 13.3 11.3
Wednesday 10.4 7.2
Samuel wants to use his earnings from Monday and Tuesday to buy some batteries that cost $5.50 each. How many batteries can Samuel buy?
Samuel can buy batteries
Answer:
I believe 2 batteries
Step-by-step explanation:
17.4 pounds from monday + 13.3 from Tuesday= 30.7 pounds.
30.7 pounds times $0.40 is $12.28
12.28/5.5 is 2.327272727...
You cant buy .3 of a batter so the answer should be 2
Albert has £500 in his savings account. His bank offers him a fixed 5% simple interest rate per annum, for a period of 5 years. How much interest will he have earned after 5 years?
Answer:
He'll earn 125 in interest after 5 years.
Step-by-step explanation:
Since it's a simple interest rate, we can use the formula to calculate the amount of interest he'll earn in those years. We have:
C = P*i*t
Where C is the amount of interest earned, P is the initial amount invested, i is the interest rate and t is the total time elapsed. For this case we have:
C = 500*0.05*5
C = 2500*0.05
C = 125
He'll earn 125 in interest after 5 years.
Can someone help me please?
Answer:
64°
Step-by-step explanation:
In circle with center P, AD is diameter.
[tex] \therefore m\angle DPE + m\angle APE = 180\degree \\
\therefore (33k-9)\degree + 90\degree = 180\degree \\
\therefore (33k-9)\degree = 180\degree -90\degree \\
\therefore (33k-9)\degree = 90\degree \\
\therefore 33k-9 = 90\\
\therefore 33k= 90+9\\
\therefore 33k= 99\\
\therefore k= \frac{99}{33}\\
\therefore k=3\\
m\angle CPD = (20k +4)\degree \\
\therefore m\angle CPD = (20\times 3 +4)\degree \\
\therefore m\angle CPD =(60+4)\degree \\
\therefore m\angle CPD =64\degree \\
m\overset {\frown}{CD} = m\angle CPD\\
\therefore m\overset {\frown}{CD} = 64\degree
[/tex]
Jessica is buying several bunches of bananas to make desserts for a fundraiser. She can buy 10 pounds of bananas at Smiths for $14.90 or 8 pounds at Walmart for $12.08. How much would the cost per pound be at Smiths?
Answer:
$1.49 per pound of bananas at Smiths
Step-by-step explanation:
1. 10 pounds is $14.90
2. Find how much one pound costs by dividing 14.90 by 10
3. 14.90/10= 1.49
4. $1.49 per pound of bananas at Smiths
Select the possible values for x in the equation x2 = 108.
A.
[tex] \sqrt[ 36]{3} [/tex]
B.
[tex] \sqrt{18} [/tex]
c. 54
D.
[tex] \sqrt[6]{3} [/tex]
Answer:
D. 6√3.
Step-by-step explanation:
x^2 = 108
x = +/- √108
x = +/- √36 * √3
x = +/- 6√3
Dr. Don offers a tutoring service for college students. He charges $40 as a fixed rate for the first hour plus $20 for each additional hour. What is the minimum and maximum number of hours of tutoring a student can get if he or she can afford to spend between $140 and $200? (Express your answer as an inequality)
Answer: 6 ≤ h ≤ 9
Step-by-step explanation:
Hi, since He charges $40 as a fixed rate for the first hour plus $20 for each additional hour, the cost of the tutoring service is equal to the fixed rate(40) plus, the product of the additional hours (h-1) and the cost per additional hour (20).
40+20(h-1)
40+20h-20
20+20h
Since a student can spend between $140 and $200, the previous expression must be greater o equal than 140, and less or equal than 200.
140≤20+20h≤200
Subtracting 20
140-20 ≤20-20+20h ≤200-20
120 ≤ 20h ≤ 180
Dividing by 20
120/20 ≤ 20h/20 ≤ 180/20
6 ≤ h ≤ 9
Final answer:
The minimum and maximum number of hours of tutoring a student can get if they can spend between $140 and $200 is 5 and 8 hours, respectively.
Explanation:
To determine the minimum and maximum number of hours of tutoring a student can get, we need to set up an inequality based on the pricing information provided. Let's denote the number of additional hours beyond the first hour as x.
The total cost of tutoring will be $40 for the first hour plus $20x for each additional hour. The student can afford to spend between $140 and $200, so the inequality is:
140 ≤ 40 + 20x ≤ 200
To find the solution, we need to isolate x. First, subtract 40 from all parts of the inequality:
100 ≤ 20x ≤ 160
Next, divide all parts of the inequality by 20:
5 ≤ x ≤ 8
Therefore, the minimum number of hours is 5 (including the first hour) and the maximum number of hours is 8 (including the first hour).
Ally slice 32 kg of watermelon for a party she divided the watermelon slices equally between 8 large bowls how many gams of watermelon did ally put in each bowl
4000 g
Step-by-step explanation:
32 kg means 32000 g of watermelon
divided into 8 bowls
grams of watermelon in each bowl are 32000÷8 = 4000 g
Ally put 4,000 grams of watermelon in each bowl.
Explanation:
To find out how many grams of watermelon Ally put in each bowl, we need to divide the total weight of the watermelon slices by the number of bowls. Ally sliced 32 kg of watermelon and divided it equally between 8 large bowls. To convert kg to grams, we multiply by 1000. So, the total weight of watermelon in grams is 32,000 grams. To find out how many grams of watermelon went into each bowl, we divide the total weight by the number of bowls: 32,000 grams / 8 bowls = 4,000 grams.
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(x+7)(x+3) polynomial standard form
Answer:
[tex] {x}^{2} + 10x + 21[/tex]
Step-by-step explanation:
[tex](x + 7)(x + 3) \\ = x(x + 3) + 7(x + 3) \\ = {x}^{2} + 3x + 7x + 21 \\ \purple{ \bold{= {x}^{2} + 10x + 21}}[/tex]
The difference of two times a number and eighteen is sixteen
Answer:
2n-18=16; n=17
Step-by-step explanation:
2n-18=16
+18 +18
2n= 34
/2 /2
n=17
Hope this helped
A butcher shop sells ground meat in 3/4 pounds packages. If the shop has 24 pounds of meat available to sell, how many packages of ground meat are for sale ?
32 packages of ground meat are for sale
What is Division?A division is a process of splitting a specific amount into equal parts.
Given that A butcher shop sells ground meat in 3/4 pounds packages
the shop has 24 pounds of meat available to sell,
We need to find the number of packages of ground meat are for sale .
To find this we have to divide 24 by 3/4
24/(3/4)
The denominator is multiplied to numerator by rationalising.
24×4/3
Twenty four times of fraction four by three.
32
Hence, 32 packages of ground meat are for sale
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There are 32 packages of ground meat for sale.
Explanation:To find the number of packages of ground meat for sale, we need to divide the total pounds of meat available by the weight of each package.
Given that each package weighs 3÷4 pounds and the shop has 24 pounds of meat available, we can divide 24 by 3÷4 to find the number of packages.
Dividing 24 by 3÷4 is the same as multiplying 24 by the reciprocal of 3÷4, which is 4÷3. Therefore, there are 24 × (4÷3) = 32 packages of ground meat for sale.
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Idk how to answer this question
Answer:
It's z^11
Step-by-step explanation:
To multiply exponents with the same base (z), you add the exponents so in this case you add 5 and 6 to get z^11
Answer:
[tex]z^{11}[/tex]
Step-by-step explanation:
[tex]z^{a} *z^{b}= z^{a+b} \\z^{5} *z^{6}= z^{5+6} = z^{11}[/tex]
Ferris wheel has a diameter of 60 ft. How far will a rider travel during a 5 minute ride if the wheel rotates once every 15 seconds?
Answer:
3769.92 ft
Step-by-step explanation:
The diameter of the wheel, d= 60 ft
We know the perimeter of the wheel is,
= πd
= 3.1416*60
= 188.496 ft
Wheel travel for 5 minutes. So the wheel travel,
= 5*60
= 300 sec
The wheel rotates in every 15 seconds. So the wheel rotates,
= 300/15
= 20 times
In one rotation, the wheel travels its perimeter. so is 5 minutes it travels,
= 188.496*20
= 3769.92 ft
X² - 24x + c
Find the answer for C.
Answer:
[tex]c=-x^{2} +24x[/tex]
Step-by-step explanation:
Subtract on both sides to isolate c.
[tex]x^{2} -24x+c\\x^{2} -24+c-c=-c\\x^{2} -24+0=-c\\x^{2} -24x=-c\\-c=x^{2} -24x[/tex]
Have c be in positive form.
[tex]-c=x^{2} -24x\\(-)(-c)=(-)(x^{2} -24x)\\c=-x^{2} +24[/tex]
The angle \theta_1θ 1 theta, start subscript, 1, end subscript is located in Quadrant \text{I}Istart text, I, end text, and \cos(\theta_1)=\dfrac{3}{8}cos(θ 1 )= 8 3 cosine, (, theta, start subscript, 1, end subscript, ), equals, start fraction, 3, divided by, 8, end fraction . What is the value of \sin(\theta_1)sin(θ 1 )sine, (, theta, start subscript, 1, end subscript, )? Express your answer exactly.
Answer:
[tex]\sin(\theta_1) =\frac{\sqrt{55} }{8}[/tex]
Step-by-step explanation:
The angle [tex]\theta_1[/tex] is located in Quadrant I and [tex]\cos(\theta_1)=\frac{3}{8}[/tex]
From Trigonometric ratio, In the First Quadrant
[tex]\cos \theta=\frac{Adjacent}{hypotenuse}[/tex]
Adjacent =3, Hypotenuse =8
Using Pythagoras Theorem
[tex]Hypotenuse^2=Opposite^2+Adjacent^2\\8^2=Opposite^2+3^2\\Opposite^2=64-9=55\\Opposite=\sqrt{55}[/tex]
Therefore:
[tex]\sin(\theta_1)=\frac{Opposite}{Hypotenuse}\\\sin(\theta_1) =\frac{\sqrt{55} }{8}[/tex]
having some trouble helppp.
Answer:
3/5
Step-by-step explanation:
Answer:
The slope is 3/5.
Step-by-step explanation:
First remember that the formula for slope is the difference in ys / difference in xs.
m = y2 - y1 / x2 - x1
Plug in the coordinates of the two points you're given, keeping in mind that coordinates are (x,y).
m = -5 - 1 / -5 -5
m = -6 / -10
m = 6/10 = 3/5
Mishka is on a long road trip, and she averages 75 mph for 2 hours while she's driving on the highway. While she's driving on side roads for 1 hour, she only averages 45 mph. What is the total distance that she covers on her road trip?
A.
120 miles
B.
195 miles
C.
240 miles
D.
75 miles
If she goes 75 mph for 2 hours, that's 150 miles altogether. 45 mph for 1 hour is 45 miles, so 150 + 45 is 195 miles.
The total distance that Mishka covers on her road trip is 195 miles.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
To calculate the total distance covered on the road trip
we need to add the distances traveled on the highway and side roads.
Distance on the highway = speed × time
= 75 mph × 2 hours
= 150 miles
Distance on side roads = speed × time
= 45 mph × 1 hour
= 45 miles
Total distance covered = Distance on the highway + Distance on side roads = 150 miles + 45 miles
= 195 miles
Therefore, the total distance that Mishka covers on her road trip is 195 miles.
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f(n) = 45 • (4/5) ^n-1
The calculated common ratio of the sequence is 4/5
How to determine the common ratio of the sequence
From the question, we have the following parameters that can be used in our computation:
[tex]F(n) = 45 \cdot (\frac45)^{n - 1}[/tex]
By definition:
A geometric sequence is represented as
[tex]F(n) = ar^{n-1}[/tex]
Where, the common ratio is r
By comparison and using the above as a guide, we have the following:
r = 4/5
Hence, the common ratio of the sequence is 4/5
Question
A sequence is defined by F(n) = 45 • (4/5) ^n-1.
What is its common ratio