Answer:
See explanation
Step-by-step explanation:
Let a,b, and c be real numbers.
The distributive property says that:
[tex]a(b + c) = ab + ac[/tex]
Assuming we want to simplify:
[tex]10(5*10^{-1}+150*10^{-3})[/tex]
We apply the distributive property to get:
[tex]10(5*10^{-1}+150*10^{-3}) = 5*10^{-1} \times 10+150*10^{-3} \times 10[/tex]
We can now use rules of exponents to simplify further:
[tex]10(5*10^{-1}+150*10^{-3}) = 5*10^{-1} \times 10^{1} +150*10^{-3} \times 10^{1} [/tex]
[tex]10(5*10^{-1}+150*10^{-3}) = 5*10^{-1 + 1} +150*10^{-3 + 1}[/tex]
[tex]10(5*10^{-1}+150*10^{-3}) = 5*10^{0} +150*10^{-2}[/tex]
[tex]10(5*10^{-1}+150*10^{-3}) = 5*1+1.50*10^{-2}x {10}^{2} [/tex]
[tex]10(5*10^{-1}+150*10^{-3}) = 5*1+1.50*10^{-2 + 2}[/tex]
[tex]10(5*10^{-1}+150*10^{-3}) = 5+1.50*10^{0} = 6.5 \times {10}^{0} [/tex]
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
Learn more:
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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
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:
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 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.
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:
The planet Mercury has a radius of 1500 miles and rotates one revolution every 1400 hours. What is the linear speed of a point on its equator in miles per hour?
The linear speed of a point on Mercury's equator is approximately 6.77 miles per hour.
To find the linear speed of a point on Mercury's equator, we can use the formula for linear speed:
[tex]\[ \text{Linear Speed} = \frac{2\pi r}{T} \][/tex]
where:
- ( r ) is the radius of the planet,
- ( T ) is the time it takes for one revolution.
Given that the radius of Mercury is 1500 miles and it rotates once every 1400 hours, we can plug in these values into the formula:
[tex]\[ \text{Linear Speed} = \frac{2\pi \times 1500}{1400} \][/tex]
Simplifying this expression gives us the linear speed in miles per hour.
[tex]\[ \text{Linear Speed} = \frac{3000\pi}{1400} \approx 6.77 \, \text{miles per hour} \][/tex]
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. :)
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.
Amelia's cell phone plans Let her send a maximum of 500 messages per month
For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 28 N acts on a certain object, the acceleration of the object is 7 /ms2. If the force is changed to 8 N, what will be the acceleration of the object?
Answer:[tex]2 m/s^{2}[/tex]
Step-by-step explanation:
According to Newton's second law, the acceleration [tex]a[/tex] of an object with mass [tex]m[/tex] is directly proporional to the force [tex]F[/tex] applied to that object:
[tex]F=m.a[/tex] (1)
In the first case we are given the following data:
[tex]F=28 N[/tex]
[tex]a=7 m/s^{2}[/tex]
Substituting this information in (1):
[tex]28 N=(m)(7 m/s^{2})[/tex] (2)
Isolating [tex]m[/tex]:
[tex]m=4 kg[/tex] (3) This is the mass of the object
Now if we keep this calculated mass, but we change the applied force to [tex]F=8 N[/tex], we will have:
[tex]8 N=(4 kg)a[/tex] (4)
Isolating the acceleration:
[tex]a=2 m/s^{2}[/tex] (5) This will be the acceleration of the object is the force is changed to 8 N.
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
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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
A customer at the mall is shopping for holiday gifts, and is considering having them wrapped. He can get them wrapped at the department store, which charges $2 per gift. Alternatively, the customer can pay his niece a flat fee of $50 to wrap all of his gifts. If he has a certain number of small packages, it would cost the same amount either way. How many small gifts would that include?
Final answer:
The customer would need to have 25 small gifts to wrap in order for the costs to be the same, whether using the department store's service at $2 per gift or paying his niece the $50 flat fee.
Explanation:
To determine how many small gifts need to be wrapped to make the cost the same whether paying his niece the flat fee of $50 or paying the department store $2 per gift, we can set up a simple equation:
Let x represent the number of small gifts.
Then, the cost of wrapping at the department store is $2 per gift, which means the cost is 2x dollars.
The niece's flat fee is $50, regardless of the number of gifts.
The equation to find the breakeven point where both options cost the same is:
2x = 50
Solving for x gives us:
x = 50 / 2
x = 25 gifts
Thus, if the customer has 25 small gifts to wrap, it would cost the same to have them wrapped by his niece at a flat rate or by the department store per gift.
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.
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
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
Find two numbers whose sum is 9 and whose difference is -1
Answer:
4 and 5
Step-by-step explanation:
Make a system of equations:
x+y=9
x-y=-1
x=9-y
9-y-y=-1
9-2y=-1
-2y=-10
y=5
Since y=5, x must be 4 since 4+5=9 and 4-5=-1
Hope this helped!
15 POINTS!
help with this. image is attached...
Answer:
50
Step-by-step explanation:
5³ ÷ (↓13 - 8) x 2
↓5³ ÷ 5 x 2
125 ÷ 5 x 2
25 x 2
50
Tiny Tim is 5 feet tall expression 0.5m + 60 can be used to calculate his height in inches if he grows an average of 0.5 inch each month. Using that expression, calculate tiny Tim’s height in 6 months.
A. 63 inches
B. 56 inches
C. 5 feet 6 inches
D. 53 inches
Answer:
The answer is A
Step-by-step explanation:
Since we are finding Tim's height in 6 months, you would have to plug the 6 into the expression.
Answer:
Step-by-step explanation: it A
0.5+6= 3
60+3= 63
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)
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]
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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In ³_/13, the 13 is called the:
radical sign
radicand
radical
index
The 13 is the radicand. The definition of radicand is "The number under the radical symbol. The correct option is B.
What is a radical expression?Any expression that contains the radical () sign is referred to as a radical expression in mathematics. This symbol, which is frequently used to calculate the square root of a number, is frequently called the "square root" symbol by mistake. But it can also refer to a cube root, a fourth root, or something higher.
The 'V'-shaped portion of the radical sign will have a superscript number when it is used to represent any root other than a square root. For instance, the expression 3(8) denotes the cube root of 8. If there is no superscript number, the square root is required by the radical expression.
The 13 is the radicand. The definition of radicand is "The number under the radical symbol.
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In the expression ³√13, the number 13 is referred to as the radicand. The radical sign (√) indicates the operation of root extraction and the number 3 stands for the index, which is the degree of the root applied to the radicand.
Explanation:In the mathematical expression ³√13, the 13 is called the radicand.
It's the number or expression underneath the radical sign (√) and it's the number you are taking the root of. In this case, we're finding the cube root of 13. The radical sign (√) itself represents the operation of root extraction. The number 3 in this instance would be known as the index, indicating the degree of the root applied to the radicand. In simpler terms, it's the number that determines what root of the radicand we are calculating.
Here, 3 means cube root.
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When Jared found 1/5 +2/5,he wrote the sum 3/10 is Jared correct
Answer:
Step-by-step explanation:
no, he is not. He literally added the numerators and the denominators. When ur adding fractions with the same denominator, u just add the numerators and keep the same denominator.
1/5 + 2/5 = 3/5
Answer:
No, because 1/5+2/5=3/5. 3/5 is also equivalent to 6/10, not 3/10.
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
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.
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
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
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