To sum the numbers in scientific notation, you add the coefficients and keep the exponent. The correct sum of 2.5 \(\times\) 10^10 and 7.8 \(\times\) 10^10, expressed in proper scientific notation, is 1.03 \(\times\) 10^11.
Explanation:To find the sum of 2.5 \(\times\) 10^10 and 7.8 \(\times\) 10^10, you add the two numbers while keeping the same exponent since they are like terms in scientific notation. You calculate 2.5 + 7.8 which equals 10.3. Therefore, the sum in scientific notation is 10.3 \(\times\) 10^10.
However, in proper scientific notation, this number should have only one non-zero digit to the left of the decimal point. So, we adjust this sum by writing it as 1.03 \(\times\) 10^11 by moving the decimal one place to the left and increasing the exponent by 1. Thus, the correct answer is 1.03 \(\times\) 10^11, which correlates with option C.
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Two-thirds (x + 6) = negative 18
Answer:
negative three and two thirds
Step-by-step explanation:
2/3(x+6)= -18
2/3x + 4 = -18
2/3x = -22
x = -3 2/3
Which expressions can be represented by the model?
Check all that apply.
10+ 4 + 10 + 4
14 x 2
18 x 2
0 24₃2
28 = 2
The expressions that can be represented by a model for the value of 28 are "10 + 4 + 10 + 4" and "14 x 2". The expression "18 x 2" equals 36 and does not represent a value of 28, and the meanings of the last two expressions ('0 24₃₂' and '28 = 2') are not clear without additional context.
To determine which expressions can be represented by a mathematical model, it's important to pay attention to the operations and numbers involved. In the list provided, there are various expressions that could potentially represent the same numerical value. For example, the expression 10 + 4 + 10 + 4 represents the sum of these numbers, which equals to 28. Similarly, 14 x 2 represents the product of 14 and 2, which also equals to 28. On the other hand, 18 x 2 equals 36, which is different from the previous two expressions.
We can look at these expressions and evaluate them:
10 + 4 + 10 + 4 = 28
14 x 2 = 28
18 x 2 = 36
Thus, from the expressions listed, only 10 + 4 + 10 + 4 and 14 x 2 can be represented by a model that reflects the value of 28. The expression 18 x 2 represents a model for the value of 36, not 28. The last two expressions, '0 24₃₂' and '28 = 2', are either typos or not clear enough to deduce a meaningful mathematical operation. If '24₃₂' indicates some form of mathematical notation or operation, it isn't standard and therefore cannot be verified without further context.
please help !!! 30 points and i’m struggling
Jane took a piece of cardboard and cut out a triangle with measures 32°, 58°, and 90°, and side lengths 5 cm, 12 cm, and 13 cm. What kind of triangle was cut out?
A.
right, scalene
B.
right, isosceles
C.
isosceles, equilateral
D.
acute, scalene
solve the simultaneous equations:
y=3x+5
y=4x²+x
Give your answer correct to 2 decimal places
Answer:answer to the questions are x=1.396 or -0.896 and y=9.188 or 2.312
Step-by-step explanation: see attachment
Thanks for drawing my attention to my mistake. I appreciate.
Answer:
The solutions (x, y) are (1.40, 9.19) and (-0.90, 2.32) correct to 2 decimal places.
Step-by-step explanation:
As the 2 expressions in x are both equal to y we can write:
4x^2 + x = 3x + 5
4x^2 - 2x - 5 = 0
x = [ -(-2) +/- sqrt(4 - 4*4*-5)] / 2*4
= 0.25 +/- (sqrt 84)/8
x = 1.396, -0.895.
When x = 1.396, y = 3(1.396) + 5 = 9.188
when x = 0.895, y = 3(-0.895) + 5 = 2.315.
On a certain hot summer's day, 391 people used the public swimming pool. The daily prices are $1.25 for children and $2.25 for adults. The receipts for admission totaled $752.75. How many children and how many adults swam at the public pool that day?
127 children and 264 adults swam at the public pool that day
Step-by-step explanation:
On a certain hot summer's day
391 people used the public swimming poolThe daily prices are $1.25 for children and $2.25 for adultsThe receipts for admission totaled $752.75We need to find how many children and how many adults swam at the public pool that day
Assume that the number of children is x and the number of adult is y in that day
∵ x children swam that day
∵ y adults swam that day
∵ 391 people used the swimming pool that day
- Add x and y, then equate the sum by 391
∴ x + y = 391 ⇒ (1)
∵ The daily price for children is $1.25 per child
∵ The daily price for an adult is $2.25
∵ The receipts for admission totaled $752.75
- Multiply x by 1.25 and y by 2.25, then add the products and
equate the sum by 752.75
∴ 1.25x + 2.25y = 752.75
- Divide each term by 1.25 to simplify the equation
∴ x + 1.8y = 602.2 ⇒ (2)
Now we have a system of equations to solve it
Subtract equation (1) from equation (2) to eliminate x
∵ (x - x) + (1.8y - y) = 602.2 - 391
∴ 0.8y = 211.2
- Divide both sides by 0.8
∴ y = 264
- Substitute the value of y in equation (1) to find x
∵ x + 264 = 391
- Subtract 264 from both sides
∴ x = 127
127 children and 264 adults swam at the public pool that day
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Cynthia plans to build a treehouse that is 1/3 the size of Andrew's tree house. Cynthia plans to make the area of her tree house at least 13 square feet. Write and solve an inequality to find the area of Andrew's tree house. Let x be the area of Andrew's tree house. Describe how you know which tree house is larger without solving the inequality.
Answer:
The area of Andrew's tree house must be greater than or equal to 117 square feet
Step-by-step explanation:
Let
x -----> the area of Andrew's tree house in square feet
y ----> the area of Cynthia's tree house in square feet
we know that
Cynthia plans to make the area of her tree house at least 13 square feet.
The word "at least" means "greater than or equal to"
so
[tex]y\geq 13[/tex] ----> inequality A
Cynthia plans to build a tree house that is 1/3 the size of Andrew's tree house
so
Remember that
When two figures are similar, the ratio of its areas is equal to the scale factor squared
In this problem the scale factor is given
The scale factor is 1/3
The scale factor squared is 1/9
That means
The area of Andrew's tree house is 9 times greater than the area of Cynthia's tree house
or
The area of Cynthia's tree house is 9 times smaller than the area of Andrew's tree house
[tex]y=\frac{1}{9}x[/tex] ----> equation B
substitute equation B in the inequality A
[tex]\frac{1}{9}x\geq 13[/tex]
solve for x
[tex]x\geq 117\ ft^2[/tex]
so
The area of Andrew's tree house must be greater than or equal to 117 square feet
we know that Andrew's tree house is larger than Cynthia's tree house, because the problem states that Cynthia's tree house is 1/3 the size of Andrew's tree house
That means
The size of Andrew's tree house is 3 times greater than the size of Cynthia's tree house, without solving the inequality
Final answer:
To find the size of Andrew's treehouse, let's assume the area as x square feet. Using the given information, we can write and solve the inequality (1/3)x ≥ 13 to find the area of Andrew's treehouse. Without solving the inequality, we know that Andrew's treehouse is larger because the area must be greater than or equal to 39 square feet.
Explanation:
To find the area of Andrew's tree house, let's assume that his tree house has an area of x square feet.
According to the information given, Cynthia plans to build a treehouse that is 1/3 the size of Andrew's tree house. Therefore, the area of Cynthia's tree house would be (1/3)x square feet.
We are told that Cynthia plans to make the area of her tree house at least 13 square feet. So we can write the inequality as follows:
(1/3)x ≥ 13
To solve the inequality, we need to multiply both sides by 3 (since the coefficient of x is 1/3). This will give us:
x ≥ 39
This means that the area of Andrew's tree house must be greater than or equal to 39 square feet.
Without solving the inequality, we can see that Andrew's tree house is indeed larger than Cynthia's tree house because the area of Andrew's tree house must be greater than or equal to 39 square feet.
marco is limited to 7 hours of screen time each week. he decides to watch a movie that is 1 hour and 20 minutes on sunday. if he divides the remainder of time equally amongst the other six days, then how many minutes can h.e watch each day? write and solve an inequality.
Marco can watch TV for at most 56 minutes each day.
Step-by-step explanation:
Given,
Time of screen each week = 7 hours
1 hour = 60 minutes
7 hours = 60*7 = 420 minutes
Length of movie = 1 hour + 20 minutes = 60 + 20 = 80 minutes
Time left for other days = 420 - 80 = 340 minutes
Number of days = 6
Let,
x be the time per day for remaining 6 days.
Number of days * Time per day ≤ Time remaining
[tex]6x\leq 340[/tex]
Dividing both sides by 6
[tex]\frac{6x}{6}\leq \frac{340}{6}\\x\leq 56.66[/tex]
Marco can watch TV for at most 56 minutes each day.
Keywords: inequality, division
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Evelyn is creating a rectangular garden in her backyard. The length of the garden is 11 feet. The perimeter of the garden must be at least 56 feet and no more than 82 feet. Use a compound inequality to find the range of values for the width w of the garden.
The range of values for the width w of the garden is 17 ≤ w ≤ 30.
Step-by-step explanation:
Given,
The length of the garden = 11 feet.
The perimeter of the garden = 56 feet (at least is the minimum value)
The perimeter of the garden = 82 feet (not more than is the maximum value)
step 1 :
Perimeter of a rectangle = 2 (length + width)
⇒ 56 = 2 (11 + width)
⇒ 56 = 22 + 2 width
⇒ 34 = 2 width
⇒ width = 34/2
∴ width = 17 feet
step 2 :
Perimeter of a rectangle = 2 (length + width)
⇒ 82 = 2 (11 + width)
⇒ 82 = 22 + 2 width
⇒ 60 = 2 width
⇒ width = 60/2
∴ width = 30 feet
step 3 :
The range of values for width 'w' is 17 ≤ w ≤ 30.
Answer:
[17,30]
Step-by-step explanation:
If 108 is 90% of x, what is the value of x?
Answer:
x=120
Step-by-step explanation:
108 = 90%
divide everything by 9
12 = 10%
multiply everything by 10
120 = 100%
x=120
Answer:
120
Step-by-step explanation:
set a relation. Because 108 is 90%, you do 90%/100% = 108/x (write vertically so its easier. So you see what number you multiply 90 by to get 108 and multiply that by 100 to get the total amount.
At a party, there are 72 people. The ratio of men to ladies to kids is 4 to 3 to 2. A) how many kids are there? B) how many men are there? C) how many ladies are there?
A) There are 16 kids.
B) There are 32 men.
C) There are 24 ladies.
Hope this helps. :)
the radius of a circle is 1 kilometer. What is the circle’s circumference?
Answer:
[tex]2\pi[/tex]
Step-by-step explanation:
Formula of circumference is [tex]C = 2\pi r[/tex]
r = radius
plug in the numbers into formula to get
[tex]2\pi (1)[/tex] which will eqaul [tex]2\pi[/tex]
Final answer:
The circumference of a circle with a radius of 1 kilometer is approximately 6.28318 kilometers, calculated using the formula C = 2πR.
Explanation:
Given that the radius of a circle is 1 kilometer, we can calculate the circumference of the circle using the formula C = 2πR, where R is the radius of the circle and π (pi) is approximately 3.14159. Since the radius is 1 kilometer, we plug that value into the formula to get:
C = 2 × 3.14159 × 1 km
C = 6.28318 km
Therefore, the circle's circumference is approximately 6.28318 kilometers.
What are the factors of -12?
Answer:
− 12 , − 6 , − 4 , − 3, −2, −1, 1, 2, 3, 4, 6 , 12
Step-by-step explanation:
-12 * 1 = -12
-6 * 2 = -12
-4 * 3 = -12
-3 * 4 = -12
-2 * 6 = -12
-1 * 12 = -12
1 * -12 = -12
2 * -6 = -12
3 * -4 = -12
4 * -3 = -12
6 * -2 = -12
12 * -1 = -12
QUESTION 2 · 0/1 POINTS
Which of the following are feasible equations of a least squares regression line for number of dollars left in an endowment
providing college scholarships in each of its first ten years if it was entirely funded by a single donation?
X
That's not right.
O
y = 269,000 + 83003
O
= 69, 000 – 83003
O
y = –269,000 - 8300.0
O
= 269,000 - 83000
O
j = 0 - 83002
(B) y = 69,000 - 8,300x
Step-by-step explanation:
Let 8,300 be the scholarship and y be the remaining amount. Also x is the number of years.
Each year, the amount 8,300 is reduced by giving the scholarship worth 8,300. Hence, the coefficient of x should be negative sign.
If the initial amount is 69,000 and the remaining amount after 10 years is negative, the regression equation is
y = 69,000 - 8,300x
Which expression is equivalent to 210d² – 63d
o
21d(10d-3)
o 21(10d+3)
o
21d(10d+3)
Answer:
21d(10d-3)
Step-by-step explanation:
21d x 10d = 210d^2
21d x 3 = -63d
so it would be 210d^2 - 63d
The expression which is equivalent to 210d² − 63d would be 21d(10d- 3).
What is factorization?factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form.
From the given expression;
210d² − 63d
A factor which is common to both terms of the expression;
21d.
On this note, the factorisation of the expression yields,
21d(10d- 3).
21d x 10d = 210d^2
21d x 3 = -63d
so it would be 210d² − 63d.
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graph the equation
Y+5= -2(x-4)
PLEASE HELP
Step-by-step explanation:
y+5-5=-2(x-4)
-5, first let's put it in the form y=mx+b.
y+5-5=-2(x-4)-5
y=-2x+3, so in this, m=slope and b=y-intercept. On your graph, plot three on the y line, and the slope is negative two, so go down two then over one to the left side, because it is decreasing. Also slope is rise over run or just rise/run.
Hope this helps, now you know the answer and how to do it. HAVE A BLESSED AND WONDERFUL DAY! As well as a great Valentines Day! :-)
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Junior has 6 baseball cards and 4 basketball cards. What fraction of Juniors cards are basketball cards?
Answer:
1/3 of his cards are basketball cards
Final answer:
Junior has 6 baseball and 4 basketball cards, making a total of 10 cards. The fraction of basketball cards is 4/10, which simplifies to 2/5, meaning 2 out of every 5 cards in Junior's collection are basketball cards.
Explanation:
Jr has 6 baseball cards and 4 basketball cards. The total number of cards Junior has is 10 (6 baseball cards + 4 basketball cards). To find out what fraction of Junior's cards are basketball cards, we divide the number of basketball cards by the total number of cards. Therefore, the fraction of Junior’s cards that are basketball cards is 4/10. This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2, resulting in a simplified fraction of 2/5. So, 2 out of every 5 cards in Junior’s collection are basketball cards.
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what is the common ratio of the sequence? -2, 6, -18, 54,..
-3
-2
3
8
Answer:
-3 (the first option)
Step-by-step explanation:
Edge 2020
how to solve −6/5x + 10= -7
Subtract 10 on both sides: -6/5x=-17
Multiply both sides by 5: -6x=-85
Divide both sides by -6: x= 14 1/6
Hope this helped!
Answer:X=6/85
Step-by-step explanation:
in right triangle ABC, angle C is a right angle, AB is 25 units long, and BC is 24 units long. What is the lenght of AC?
Answer:
7 units long
Step-by-step explanation:
We are given a right triangle ABC
AB = 25 units BC = 24 unitsWe are required to determine the length of AC
We are going to use the Pythagoras theorem;According to the theorem, if a and b are the legs of a right triangle and c is the hypotenuse, then;a² + b² = c²
In this case;
AB is the hypotenuse and BC is one of the legs of the triangle;
Therefore;
AB² = BC²+AC²
Rearranging the formula;
AC² = AB² - BC²
= 25² - 24²
= 625 - 576
= 49
AC = √49
= 7
Thus, AC is 7 units long
Amelia's cell phone plans Let her send a maximum of 500 messages per month
Question 2 of my ready pretty easy question im just dumb
Answer:
I think the answer is B.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
x² + y² = z² , substitute values
4² + y² = ([tex]\sqrt{137}[/tex] )², that is
16 + y² = 137 ( subtract 16 from both sides )
y² = 121 ( take the square root of both sides )
y = [tex]\sqrt{121}[/tex] = 11 → D
can I get some help, I don't understand what I'm supposed to do here. if you're curious the answers are: x=6 y=5
x=7y=8
x=6 y=6 and x=6 y=8 but I honestly don't think any of these are right
Answer:
x=6
y=5
Step-by-step explanation:
15x=90 (corresponding angles)
x=90/15
x=6
Now
5x+12y=90(vertical angles)
5(6)+12y=90
30+12y=90
12y=90-30
12y=60
y=5(dividing both sides by 12)
if x+7=23,then x=16 what property is this
The property used in this equation is the addition property of equality.
Explanation:The property used in this equation is called the addition property of equality. According to this property, if two numbers are equal, then adding the same number to both sides of the equation will still result in an equality.
In the given equation, x + 7 = 23, we need to isolate the variable x. To do this, we can subtract 7 from both sides of the equation, using the subtraction property of equality. This simplifies the equation to x = 16.
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find the slope of the line passing through the points (-4, 6) and (3, -8)
Answer:
The slope of the line is 2.
Step-by-step explanation:
slope = y2 - y1/x2 - x1
= -8 - 6/3 - (-4)
= 14/3 + 4
= 14/7
= 2
Answer: Use the slope formula to find the slope m .
m = -2
Step-by-step explanation:
8. Given the standard deviation of 16 for a population and a 95% confidence level, find the margin
of error of a sample space containing 60 values.
(1 point)
4.0486
3.3979
0.5227
29.4000
Answer:
4.0486
Step-by-step explanation:
The margin of error is calculated using [tex]E=z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} }[/tex]
Where n=60 is the sample size and [tex]\sigma=16[/tex] is the population standard deviation.
The critical value corresponding to 95% confidence interval is [tex]z_{\frac{\alpha}{2}}=1.96[/tex]
We substitute the values to obtain;
[tex]E=1.96*\frac{16}{\sqrt{60} }[/tex]
[tex]E=1.96*2.06559=4.0486[/tex]
The height of a parallelogram is 10ft more than its base
The area is 1200ft
Solve b and h
Answer:
The answer is b = 30 ft and h = 40 ft.
Step-by-step explanation:
Given:
The height of a parallelogram is 10ft more than its base
The area is 1200 ft².
Now, to solve for b and h.
Let the base (b) be [tex]x.[/tex]
And the height (h) is = [tex]x+10.[/tex]
Area = 1200 ft².
Now, to solve we put formula of area:
[tex]Area =b\times h[/tex]
[tex]1200=x\times (x+10)[/tex]
[tex]1200=x^2+10x[/tex]
Subtracting both sides by 1200 we get:
[tex]0=x^2+10x-1200\\x^2+10x-1200=0[/tex]
Now, solving the quadratic equation:
[tex]x^2+40x-30x-1200=0[/tex]
[tex]x(x+40)-30(x+40)=0[/tex]
[tex](x+40)(x-30)=0[/tex]
[tex]x+40=0[/tex] and [tex]x-30=0[/tex]
Subtracting Adding both sides
both sides by 30 we get:
by 40 we get:
[tex]x=-40.[/tex] [tex]x=30.[/tex]
So, we will take the positive result.
[tex]x=30.[/tex]
Thus, the base (b) = 30 ft.
Now, getting the height (h) by substituting the value of [tex]x[/tex]:
[tex]x+10\\=30+10\\=40\ ft.[/tex]
Therefore, the answer is b = 30 ft and h = 40 ft.
solve 6x^2 - 42 = 0 for the exact values of x
Answer:
The values of x are
[tex]x=-\sqrt{7} , x=\sqrt{7}[/tex]
Step-by-step explanation:
we have
[tex]6x^{2}-42=0[/tex]
Solve for x
Adds 42 both sides
[tex]6x^{2}-42+42=0+42[/tex]
[tex]6x^{2}=42[/tex]
Divide by 6 both sides
[tex]6x^{2}/6=42/6[/tex]
simplify
[tex]x^2=7[/tex]
square root both sides
[tex]x=\pm\sqrt{7}[/tex]
therefore
The values of x are
[tex]x=-\sqrt{7} , x=\sqrt{7}[/tex]
The exact solution for the values of x in the given equation are: +√7 and -√7.
What are the exact values of x in the equation?From the task content; it follows that the given equation is; 6x² - 42 = 0.
On this note, the evaluation for the values of x can be done as follows;
6x² - 42 = 0
6x² = 42
x² = 7
x = ±√7.
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Find the discriminant. 2p^2-9p+8=0
Answer:
Step-by-step explanation:
2p^2-9p+8=0
(2p^2-p)-(8p+8)=0
2p(p-1)-8(p-1)=0
(2p-8) (p-1)=0
2p-8=0
2p=8
P=8/2
P=4
Or
P-1=0
P=0+1
P=1
At the recent cross country banquet, people could choose to have eat chicken or beef. In total 18 out of 30 people chose beef what percent of choose chicken ?
Answer:
12
Step-by-step explanation:
All you have to do is subtract 30 and 18 and your answer is 12.
Answer:
2/5 or 40%
Step-by-step explanation:
Take 18 away from 30 to find out the missing value of 12, and simplify to get a fraction. For a decimal input into calculator and multiply by 100