Answer:The value of f is;
Step-by-step explanation:
f=1/t
At the Idaho Humane Society there is a ratio of 9 cats 13 dogs . If there are a total of 66 cats and dogs how many are cats ?
Answer:
27 cats.
Step-by-step explanation:
The fraction of cats = 9 / (9 + 13) and dogs = 13 / ( 9 + 130
= 9/22 and 13/22
So the number of cats = (9/22) * 66
= 9 *3
= 27.
=
Write in standard form (100 x 3)+(4 x 0.1)+(7 x 0.001)
Answer:
300.407
Step-by-step explanation:
100*3=300
4*0.1=0.4
7*0.001=0.007
----------------------
300+0.4+0.007
300.407
More than 450 students went on a field trip. Ten buses were filled and 5 more students traveled in a car. How many students were on each bus?
Answer:a total of 45 students per bus
Step-by-step explanation: 450-5= 445
445/10= 44.5
a total of 45 students per bus
please help!!! due tonight
Answer:
[tex]A=10^0[/tex]
Step-by-step explanation:
Number 2.247 has 2 in ones place, 2 in tenths place, 4 in hundredths place and 7 in thousandths place.
This means you can rewrite this number as
[tex]2.247=2\times 1+2\times 0.1+4\times 0.01+7\times 0.001\\ \\2.247=2\times 10^0+2\times \dfrac{1}{10^1}+4\times \dfrac{1}{10^2}+7\times \dfrac{1}{10^3}[/tex]
So,
[tex]A=10^0\\ \\B=\dfrac{1}{10^1}\\ \\C=\dfrac{1}{10^2}\\ \\D=\dfrac{1}{10^3}[/tex]
The lunch lady has 8 pounds of lasagna. If she makes 1/5-pound servings using this amount of lasagna, how many servings can she make?
Answer:
40
Step-by-step explanation:
8 / (1/5)
When dividing fractions, the second fraction just flips upside down. Then you just multiply.
So it's now 8 * 5 = 40
[tex]\frac{x^{\frac{5}{6} } }{x^{\frac{1}{6} } }[/tex]
Answer:
x^2/3
Step-by-step explanation:
(x^5/6)/(x^1/6)=x^(5/6-1/6)=x^4/6
simplify 4/6, you get 2/3.
a. Original Price: $16.20
Increase by 40%
Final Price:
Proportional Constant:
How to find the final price and the constant of proportionality in this problem?
Answer:
The final price is $ 22.68 And Proportional constant is 1.4
Step-by-step explanation:
Given as :
The Original price = $ 16.20
The rate of increase = 40%
Let The final price = x
Now,
Final price after increase = initial price × ( 1 + [tex]\frac{\textrm Rate}{100}[/tex]
Or. Final price after increase = $ 16.20 × ( 1 + [tex]\frac{\textrm 40}{100}[/tex]
Or, Final price after increase = $ 16.20 × ( 1.4 )
∴ Final price after increase = $ 22.68
Now , Proportional constant = [tex]\frac{22.68}{16.20}[/tex]
I.e Proportional constant = 1.4
Hence The final price is $ 22.68 And Proportional constant is 1.4 Answer
A random sample is used to estimate the mean time required for caffeine from products such as coffee or soft drinks to leave the body after consumption. A 95% confidence interval based on this sample is: 5.6 hours to 6.4 hours (for adults).
Answer:
Sample size n = 96.04
Explanation:
Given the interval is 5.6 hours to 6.4 hours
Let x be the midpoint, then x = (5.6+6.4)/2 = 6
Let E be the radius, then E = (6.4-5.6)/2 = 0.8/2 = 0.4
σ = 2 hours; as standard deviation is given and α = 0.05
Therefore, the sample size is:
[tex]n=\left(\frac{1.96 * 2}{0.4}\right)^{2}=96.04[/tex]
The student's question pertains to a 95% confidence interval estimate of the mean time required for caffeine to leave the body after consumption, which was found to be 5.6 to 6.4 hours in adults. This suggests that if the study were conducted multiple times, the mean time for caffeine to leave the body would lie within this range in 95% of those studies. The influence of variances in individual's metabolism, body mass, and general health can impact the range of the confidence interval.
Explanation:The subject of this discussion revolves around statistics and more specifically around the concept of confidence intervals. In the provided context, researchers conducted a study to estimate the mean time it takes for an adult body to process and remove caffeine. They found, with a 95% confidence interval, that this time lies between 5.6 hours and 6.4 hours.
This means that if the researchers were to conduct this study multiple times, in 95% of those studies, the mean (average) time for caffeine to leave the body would lie within that given range (5.6 to 6.4 hours). This is a common method in statistics and is used as a way to give an estimate about where the actual (population) value might lie in the context of sampling error.
However, it's important to note that variance in the sample population can impact the confidence interval. Individual differences such as metabolism rate, body mass, and overall health can influence how quickly a person processes caffeine, which may result in a wider confidence interval.
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4×=32 how do i solve this
Answer:
x=8
Step-by-step explanation:
You divide both sides by 4 to get x alone.
Answer:
x = 8
Step-by-step explanation:
4x divied by 4 is x. 32 divided by 4 is 8.x = 8Find the length of PQ if PQ parallel to BC and PQ is a midsegment of ABC
Answer:
4.924 units.
Step-by-step explanation:
See the attached diagram.
If P is the midpoint of AB and Q is the midpoint of AC, then PQ is parallel to BC and the length of PQ will be half of BC.
Now, the coordinates of B are (1,1) and that of C is (10,-3).
Therefore the length of BC is [tex]\sqrt{(10 - 1)^{2} + (- 3 - 1)^{2}} = 9.848[/tex] units (Approximate)
Therefore, the length of PQ = 0.5 × 9.848 = 4.924 units. (Answer)
We know that the distance between two given points ([tex]x_{1},y_{1}[/tex]), and ([tex]x_{2},y_{2}[/tex]) is given by the formula
[tex]\sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}}[/tex]
Algebra 2! please help!
What is the result of dividing x3−4 by x + 2?
x2−2x+4+4x+2
x2−2x+4+12x+2
x2−2x+4−12x+2
x2−2x+4−4x+2
Answer:
Choice C)
x^2 - 2x + 4 - 12/(x+2)
[tex]x^2 - 2x + 4 - \frac{12}{x+2}[/tex]
====================================================
Explanation:
To see how I got that answer, I have provided two attached images below. One of them shows the polynomial long division. The other shows synthetic division. Both are valid options to get to the same answer.
For each method, I used 1x^3 + 0x^2 + 0x - 4 in place of x^3 - 4 so that the proper terms could align.
In which step to the student first make an error and what is the correct step
Answer:
step 2 i believe
Step-by-step explanation:
hope this helps
Answer:
The answer is B
Step-by-step explanation:
Hope this helps :))
Which change (in percent) is larger: losing weight from 100 lb to 90 lb or losing weight from 50 lb to 40 lb
Answer: losing weight from 50lb to 40lb
Step-by-step explanation:
Answer:
50lb to 40lb
Step-by-step explanation:
When you multiply 50 lb to 40lb by 2, it makes 100 lb to 80 lb. 50lb to 40 lb is 20 percent change while 100 lb to 90 lb is 10 percent
6. Savannah leaves Redlands driving due north at
55 mph. Luke leaves Redlands at the same time
and drives due south at 62 mph. How far apart
are they after 3 hours?
8 is 25% of what number?
Answer: The answer is 32
Answer:
32
Step-by-step explanation:
25%=0.25
8/0.25=32
What is the solution to this equation x/-3=6
Answer:
[tex]\frac{x}{-3} =6\\x=-18[/tex]
x= -18
Answer: X = -18
Step-by-step explanation: In this problem, notice that x is being divided by -3 so to get x by itself, we need to multiply both sides of the equation by -3.
Notice that on the left side, the -3 and -3 cancel each other out so we're just left with x.
On the right side, we have 6 × -3 which is -18 so X = -18.
Finally, we can check our answer by plugging a -18 back into the original equation.
So we have -18 ÷ -3 = 6, which is a true statement which means that our answer is correct.
Image provided.
A financial advisor tells you that you can make your child a millionaire if you just start saving early. You decide to put an equal amount each year into an investment account that earns 7.5% interest per year, starting on the day your child is born. How much would you need to invest each year (rounded to the nearest dollar) to accumulate a million for your child by the time he is 35 years old? (Your last deposit will be made on his 34th birthday.)
Answer:
$12159 per year.
Step-by-step explanation:
If I invest $x each year at the simple interest of 7.5%, then the first $x will grow for 35 years, the second $x will grow for 34 years and so on.
So, the total amount that will grow after 35 years by investing $x at the start of each year at the rate of 7.5% simple interest will be given by
[tex]x( 1 + \frac{35 \times 7.5}{100}) + x( 1 + \frac{34 \times 7.5}{100}) + x( 1 + \frac{33 \times 7.5}{100}) + ......... + x( 1 + \frac{1 \times 7.5}{100})[/tex]
= [tex]35x + \frac{x \times 7.5}{100} [35 + 34 + 33 + ......... + 1][/tex]
= [tex]35x + \frac{x \times 7.5}{100} [\frac{1}{2} (35) (35 + 1)][/tex]
{Since sum of n natural numbers is given by [tex]\frac{1}{2} (n)(n + 1)[/tex]}
= 35x + 47.25x
= 82.25x
Now, given that the final amount will be i million dollars = $1000000
So, 82.25x = 1000000
⇒ x = $12,158. 05 ≈ $12159
Therefore. I have to invest $12159 per year. (Answer)
Should a denominator or numerator be bigger?
Answer: Usually, a denominator should be bigger. If the numerator was bigger, it would make the fraction inproper, which you should convert into a mixed number.
Answer:denominator
Step-by-step explanation:
The following ratios form a proportion. 5/18 = 10/90
True or False
13 pts.
Answer:
False
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
Leonard it sells small watermelons for seven dollars each and large watermelons for $10 each one day the number of small watermelons he saw was 15 more than the number of large watermelons and he made a total of $394 how many small and how many large watermelons a did he sell?
He sold 32 small watermelons and 17 large watermelons.
Step-by-step explanation:
Let,
Small watermelons = x
Large watermelons = y
Cost of one small watermelon = $7
Cost of one large watermelon = $10
According to given statement;
x = y+15 Eqn 1
7x+10y=394 Eqn 2
Putting value of x from Eqn 1 in Eqn 2
[tex]7(y+15)+10y=394\\7y+105+10y=394\\17y=394-105\\17y=289\\[/tex]
Dividing both sides by 17
[tex]\frac{17y}{17}=\frac{289}{17}\\y=17[/tex]
Putting y=17 in Eqn 1
[tex]x=17+15\\x=32[/tex]
He sold 32 small watermelons and 17 large watermelons.
Keywords: linear equations, substitution method
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Lin is making a window covering for a window that has the shape of a half circle on top of a square of side length 3 feet. How much fabric does she need
Answer:
Lin needs 12.53 square feet of fabric
Step-by-step explanation:
we know that
The area of the window covering is equal to the area of the square plus the area of semicircle
step 1
Find the area of the square
The area of the square is equal to
[tex]A_1=b^{2}[/tex]
where
b is the length side of the square
we have
[tex]b=3\ ft[/tex]
substitute
[tex]A_1=3^{2}=9\ ft^2[/tex]
step 2
Find the area of semicircle
The area of semicircle is equal to
[tex]A_2=\frac{1}{2}\pi r^{2}[/tex]
The length side of the square is equal to the diameter of semicircle
so
[tex]r=3/2=1.5\ ft[/tex] ----> the radius is half the diameter
assume
[tex]\pi =3.14[/tex]
substitute
[tex]A_2=\frac{1}{2}(3.14)(1.5)^{2}[/tex]
[tex]A_2=3.53\ ft^2[/tex]
Adds the areas
[tex]A=A_1+A_2[/tex]
[tex]A=9+3.53=12.53\ ft^2[/tex]
therefore
Lin needs 12.53 square feet of fabric
Final answer:
Lin needs approximately 12.54 square feet of fabric for a window covering with a half-circle on top of a square, both with a side length of 3 feet. Calculating the areas of the square and the half-circle and summing them gives the total fabric required.
Explanation:
To calculate the amount of fabric Lin needs for the window covering with a half-circle on top of a square with a side length of 3 feet, we need to find the area of both the square and the half-circle and add them together. The area of the square is straightforward - since all sides are equal, the area is side × side, which is 3 feet × 3 feet = 9 square feet. For the half-circle, we first need to calculate the area of a full circle using the formula πr² (where π is pi, approximately 3.14159, and r is the radius of the circle). The diameter of the circle is the same as the side length of the square, which is 3 feet, making the radius 1.5 feet.
So, the area of a full circle is π × (1.5 feet)² = π × (2.25 square feet).
To find the area of the half-circle, we simply divide this by 2, resulting in π × 2.25 square feet / 2 = 3.53429174 square feet. Adding the area of the square and the half-circle gives us the total fabric needed: 9 square feet + 3.53429174 square feet = 12.53429174 square feet.
Therefore, Lin needs approximately 12.54 square feet of fabric for her window covering.
If s(x) = 2x2 + 3x - 4, and t(x) = x + 4 then s(x) · t(x) =
Answer:
[tex]\large\boxed{s(x)\cdot t(x)=2x^3+11x^2+8x-16}[/tex]
Step-by-step explanation:
[tex]s(x)=2x^2+3x-4,\ t(x)=x+4\\\\s(x)\cdot t(x)\\\\\text{use the distributive property:}\ a(b+c)=ab+ac\\\\s(x)\cdot t(x)=(2x^2+3x-4)(x+4)\\\\=(2x^2+3x-4)(x)+(2x^2+3x-4)(4)\\\\=(2x^2)(x)+(3x)(x)+(-4)(x)+(2x^2)(4)+(3x)(4)+(-4)(4)\\\\=2x^3+3x^2-4x+8x^2+12x-16\\\\\text{combine like terms}\\\\=2x^3+(3x^2+8x^2)+(-4x+12x)-16\\\\=2x^3+11x^2+8x-16[/tex]
Final answer:
The product of the functions [tex]s(x) = 2x^2 + 3x - 4[/tex] and t(x) = x + 4 is obtained by multiplying each term of s(x) with each term of t(x), resulting in [tex]2x^3 + 11x^2 + 8x - 16[/tex].
Explanation:
To find the product of s(x) and t(x), given [tex]s(x) = 2x^2 + 3x - 4[/tex], and t(x) = x + 4, we use the distributive property to multiply each term in s(x) by each term in t(x). The steps are as follows:
Multiply [tex]2x^2[/tex] (the first term of s(x)) by x (the first term of t(x)) to get [tex]2x^3[/tex].Multiply [tex]2x^2[/tex] by 4 (the second term of t(x)) to get [tex]8x^2[/tex].Multiply 3x (the second term of s(x)) by x to get [tex]3x^2[/tex].Multiply 3x by 4 to get 12x.Multiply -4 (the third term of s(x)) by x to get -4x.Multiply -4 by 4 to get -16.Adding up all these products:
[tex]2x^3 + (8x^2 + 3x^2) + (12x - 4x) - 16[/tex]
Simplifying:
[tex]2x^3 + 11x^2 + 8x - 16[/tex]
Thus, the product s(x) · t(x) is [tex]2x^3 + 11x^2 + 8x - 16[/tex]
The length of a rectangle is 1.3 feet, and the width is 2.1 feet. What is the perimeter
10.
Your brother has $2000 saved for a vacation. His airplane ticket is $637. Write and solve an
inequality to find how much he can spend for everything else.
Answer:
He can spend $1363 for everything else.
Step-by-step explanation:
x+637<=2000
x<=2000-637
x<=1363
Find the slope and reduce.
P=(4.5,-1) Q=(5.3,2)
Answer: slope m = (y2 - y1)/(x2 - x1) so that m = (2-(-1))/(5.3-4.5)
m = 3 / .8 = 3.75 or 15/4
Step-by-step explanation:
Find the output, h, when the input, x, is -18. h = 17+x\6
Answer:
[tex]17 + \frac{ - 18}{6} = 17 - 3 = 14[/tex]
How many inches are equivalent to 2 meters?
Round your answer to the nearest tenth.
The measurement 2 meters is equivalent to
inches.
To convert 2 meters to inches, you multiply by the conversion factor of approximately 39.37, resulting in 78.7 inches when rounded to the nearest tenth.
The measurement 2 meters is equivalent to
78.7 inches.
To convert meters to inches, we know that 1 meter is approximately 39.37 inches. Therefore, 2 meters would be equal to 2 x 39.37 = 78.74 inches. Rounding to the nearest tenth, this equals 78.7 inches.
Kay has 28 coins which includes nickels and dimes if the total is 2.35$, how many of each coin does Kay have?
Answer:9 nickels and 19 dimes.
Step-by-step explanation:
Let [tex]n[/tex] be the number of nickels Kay has.
Let [tex]d[/tex] be the number of dimes Kay has.
Value of [tex]1[/tex] nickel is $[tex]0.05[/tex]
Value of [tex]n[/tex] nickels is $[tex]0.05n[/tex]
Value of [tex]1[/tex] dime is $[tex]0.1[/tex]
Value of [tex]d[/tex] nickels is $[tex]0.1dn[/tex]
Given that Kay has a total of [tex]28[/tex] coins.
So,[tex]n+d=28[/tex] ...(i)
Given that Kay has a total value of $[tex]2.35[/tex]
So,[tex]0.05n+0.1d=2.35[/tex] ...(ii)
Using (i) and (ii),
[tex]0.05n+0.1(28-n)=2.35\\0.05n+2.8-0.1n=2.35\\2.8-2.35=0.05n\\0.45=0.05n\\n=9[/tex]
[tex]d=28-n=28-9=19[/tex]
What is the relationship between the sides of a right triangle?
Answer:
⇒[tex](Base)^2 + ( Perpendicular)^2 = (Hypotenuse)^2[/tex] is the required relationship.
Step-by-step explanation:
Let us assume, the given right angled triangle is ΔPQR.
Here. PQ = Perpendicular of the triangle.
QR = Base of the triangle.
PR = Hypotenuse of the triangle.
Now, PYTHAGORAS THEOREM states:
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“
⇒[tex](Base)^2 + ( Perpendicular)^2 = (Hypotenuse)^2[/tex]
Hence in ΔPQR: [tex](QR)^2 + ( PQ)^2 = (PR)^2[/tex]
And the above expression is the required relationship between the sides of a right triangle.
The sides of a right triangle have a specific relationship given by the Pythagorean Theorem, which states a² + b² = c², where a and b refer to the lengths of the sides and c refers to the length of the hypotenuse. Additionally, the sides have relationships to the angles of the triangle expressed through trigonometric functions.
Explanation:The relationship between the sides of a right triangle is given by the Pythagorean Theorem which was demonstrated by the ancient Greek philosopher, Pythagoras. This theorem states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In mathematical terms, if the lengths of the sides are a, b, and c (where c represents the length of the hypotenuse), then the relationship can be represented as a² + b² = c².
Moreover, the sides of a right triangle also have specific relationships to the measures of the angles of the triangle, which are expressed through the trigonometric functions sine, cosine, and tangent. For example, for an angle in a right triangle, the sine is the length of the opposite side divided by the length of the hypotenuse, the cosine is the length of the adjacent side divided by the hypotenuse, and the tangent is the length of the opposite side divided by the adjacent side.
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Gabriela has dinner at a cafe and the cost of her meal is
$
45.00
$45.00dollar sign, 45, point, 00. Because of the service, she wants to leave a
15
%
15%15, percent tip.
What is her total bill including tip?
Answer:
Step-by-step explanation:
Answer:
Total bill=$51.75
Step-by-step explanation:
Step 1: Determine the cost of her meal
Cost of meal=$45
Step 2: Calculate the amount of the tip
Tip amount=15% of the cost of meal
where;
cost of meal=$45
replacing;
Tip amount=(15/100)×45=6.75
The tip amount=$6.75
Step 3: Total bill
The total bill can be expressed as;
Total bill=tip amount+subtotal
where;
tip amount=$6.75
cost of meal=$45
replacing;
Total bill=(45+6.75)=51.75
Total bill=$51.75