which expression is equivalent to (4h^7k^2)^4?
A: 16h^11k^6
B: 16h^28k^8
C; 256h^11k^6
D: 256h^28k^8
Answer: Option 'D' is correct.
Step-by-step explanation:
Since we have given that
[tex](4h^7k^2)^4[/tex]
We need to simplify this :
Here we go:
We will apply :
[tex](a^m)^n=a^{mn}[/tex]
[tex](4h^7k^2)^4\\\\=4^4\times (h^7)^4\times (k^2)^4\\\\=256h^{28}k^8[/tex]
Hence, option 'D' is correct.
on a certain planet, objects weight about 7/12 of what they weigh on earth. an object weights 13 5/12 pounds on the planet. solve the equation 7/12 w= 13 5/12 for w to find the objects weight on earth in pounds.
What is the value of a?
Which of the following is the conjugate of a complex number with 2 as the real part and −8 as the imaginary part?
The conjugate of the given complex number is:
[tex]2+8i[/tex]
Step-by-step explanation:We know that any complex number is written in the form of:
[tex]z=a+ib[/tex]
where a and b are real numbers.
The conjugate of the complex number is given by:
[tex]\bar z=\bar {a+ib}\\\\i.e.\\\\\bar z=a-ib[/tex]
Here we are given that:
We have a complex number such that the real part of a complex number is 2 and it's imaginary part is -8.
i.e.
a=2 and b= -8
i.e. the complex number is:
[tex]z=2+(-8)i[/tex]
Hence, the conjugate of this number is:
[tex]\bar z=2-(-8)i\\\\i.e.\\\\\bar z=2+8i[/tex]
can anone help me please
a. The perimeter of the triangle is 18 cm. b. The area of the triangle is 24 cm². c. Tiling the triangle at $7 per square centimeter would cost $168.
a. Perimeter:
Perimeter} = 5 + 5 + 8 = 18 cm
b. Area:
Use Heron's formula since the sides are known:
[tex]\[ s = \frac{5 + 5 + 8}{2} = 9 \] \[ \text{Area} = \sqrt{s(s-5)(s-5)(s-8)} \] \[ \text{Area} = \sqrt{9 \times 4 \times 4 \times 1} = \sqrt{576} = 24 \, \text{cm}^2 \][/tex]
c. Cost to Tile:
If the cost is $7 per square centimeter:
[tex]\[ \text{Cost} = \text{Area} \times \text{Cost per square centimeter} \] \[ \text{Cost} = 24 \times 7 = 168 \][/tex]
Therefore,
a. Perimeter = 18 cm
b. Area = 24 cm²
c. Cost to Tile = $168
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A triangle has a perimeter of 10x+2. Two sides have lengths of 5x and 2x+9. What is the length of the 3rd side?
In dogs, the drug carprofen has a half-life of 8 hours. If a veterinarian gives a dog an 80-milligram dose, how long will it take for the amount of carprofen in the dog to reach 10 milligrams?
Final answer:
Using the half-life formula, it would take 24 hours for the amount of carprofen to reduce from an initial dose of 80 milligrams to 10 milligrams.
Explanation:
To calculate the time it will take for the amount of carprofen to decrease from 80 milligrams to 10 milligrams in a dog, given the half-life of 8 hours, the exponential decay formula can be used. The half-life formula is:
[tex]C = C0 \times (1/2)^{(t/T)[/tex]
C is the final concentration of the drug.C0 is the initial concentration of the drug.t is the time elapsed.T is the half-life of the drug.Let's set up the equation using the given values:
[tex]10 mg = 80 mg \times (1/2)^{(t/8 hours)[/tex]
Now, we solve for t:
[tex]10/80 = (1/2)^{(t/8)[/tex]
[tex]1/8 = (1/2)^{(t/8)[/tex]
To find the exponent t/8 that makes this equation true, we can use logarithms:
log2(1/8) = t/8
-3 = t/8
t = -3 * 8
t = -24 hours
The negative result is due to the fact that we are finding a factor by which the concentration is reduced. To get the actual time elapsed, we take the absolute value:
t = 24 hours
Therefore, it would take 24 hours for the amount of carprofen to reduce to 10 milligrams.
"if z is a standard normal variable, find the probability. the probability that z lies between 0 and 3.01"
The probability that z lies between 0 and 3.01 P(0<z<3.01) = 0.4987.
What is z- score?The Z-score quantifies the discrepancy between a given value and the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations a specific data point deviates from the mean. In essence, standard deviation represents the degree of variability present in a given data collection.
Given:
Probability between z = 0 and z = 3.01 is given by
As, P(0<z<3.01)
= P(z<3.01) - P(z<0)
So, the z score values are
P(z<0) = 0.5
and, P(z<3.01) = 0.9987
Hence, the probability that z lies between 0 and 3.01 P(0<z<3.01) = 0.4987.
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what is the other measurement of the shape?
for the length of the side that is not given:
look at it as part of a triangle with the legs being 4m tall by 6 m wide
so 4^2 + 6^2 = X62
16+36 = 52^2
square root(52) = 7.211 m
does it as to round of to nearest whole number? nearest tenth?
round off answer as needed
A circular fountain has a circular walkway surrounding it with a width of 7 ft. The total area taken up by the walkway is 693π ft^2. Find the diameter of the pool.
The ordered pair (a, b) gives the location of point P on the coordinate plane. The value of a is negative and the value of b is zero. Where could point P be located on the coordinate plane?
Select one or more:
Quadrant I
Quadrant II
Quadrant IV
Quadrant III
x-axis
y-axis
Answer:
X-axis.Step-by-step explanation:
Givens
We have point which coordinates are (a,b)The value of a is negative.The value of b is zero.Now, remember that all coordinates with the form (a,0), represents points on the x-axis, because the y-coordinate is zero.
In this case, we have negative horizontal coordinates and a null vertical coordinate, like (-a,0).
This points is on the x-axis, because y-value is null. Actually, it's on the negative part of x-axis, because its horizontal coordinate is negative.
Therefore, the right answer is x-axis.
The car salesman tells you that the car can go from a stop position to 60 mph in six seconds he's giving you the cars rate of
Answer:
acceleration i think
Step-by-step explanation:
when I make macaroni and cheese for my brother and me, I use 2 2/3 tablespoons of butter. how much butter will I n need to make my macaroni and cheese dish for Thanksgiving dinner if 15 people are attending?
To keep heating costs down for a structure, architects want the ratio of surface area to volume as small as possible. An expression for the ratio of the surface area to volume for the square prism shown is . Find the ratio when b = 12 ft and h = 18 ft.
How long will it take a bird traveling at an average speed of 12 miles per hour to travel 202 miles while flying south for winter?
Answer:
16 50 min
Step-by-step explanation:
During a sale, a dress decreased in price from $90 to &63. What was the percent of decrease?
Can two numbers have a GCF that is bigger than their LCM? Explain how you know?
1. An elf, a dwarf, a hobbit, a wizard, and a man are sitting in a line. How many different ways can they sit if the elf and the dwarf insist on sitting next to each other?
a. 6 ways
b. 48 ways
c. 36 ways
d. 12 ways
e. 24 ways
2. How many ways can you order a hamburger of you can order it with or without cheese, lettuce, tomatoes, pickles, or onions?
a. 10
b. 32
c. 64
d. 5
Final answer:
In this question, the arrangements of characters sitting together and the options for hamburger toppings are explored using permutations and combinations in Mathematics for High School.
Explanation:
(1) When the elf and the dwarf insist on sitting next to each other, treat them as one entity. Then, there are 4 entities: {elf & dwarf}, hobbit, wizard, man. This gives 4! ways to arrange them, and the elf and dwarf can be arranged within their entity in 2! ways.
So, the total ways are 4! x 2! = 48 ways.
(2) For the hamburger order, since you can choose to include/exclude each topping independently, there are 2 options for each topping (with or without).
Hence, the total ways to order the hamburger are 2⁵ = 32 ways.
Use the number 913,256. Write the name of the period that has the digits 913.
Two standard number cubes are thrown, one after the other. What is the probability that the first cube lands showing a 1 and the second cube lands showing a number that is not 1? Round the answer to the nearest thousandth.
Answer:
B on edge
Step-by-step explanation:
which expression represents the distance between the two points x and y on the number line -4 and 3
Answer with explanation:
The two points on the number line are
x = -4
y=3
The distance is a positive Quantity.
So, Distance between x and y can be written as:
=|x-y| or |y-x|
=|3-(-4)| or |-4-3|
=|3+4| or |-7|
=|7| or |-7|
=7 Units
The expression will be : =|x-y| or |y-x|
=|3-(-4)| or |-4-3|
Let g(x) = x - 3 and h(x) = x2 + 6. What is (h o g)(1)?
The sum of two consecutive even integers equals 6426?
Which measure of variability is the most appropriate for this set of values?
13, 42, 104, 36, 28, 6, 17
Answer:
in other words that guy said E
Step-by-step explanation:
The circle will be dilated by a scale factor of 6. What is the value for n if the expression nPI represents the circumference of the circles in inches?
The value of n is 12 .
What is scale factor?The scale factor is a measure for similar figures, who look the same but have different scales or measures. Suppose, two circle looks similar but they could have varying radii. The scale factor states the scale by which a figure is bigger or smaller than the original figure.
According to the question
The circle will be dilated by a scale factor of 6 .
so,
New radius of the circle R = 6r
As is it dilated by a scale factor of 6
Now ,
The circumference of the new circles = 2πR
= 2.6π
= [tex]12\pi r[/tex] -------------------- (1)
and given circumference of the new circles = nπ ---------------------(2)
when we compare both n = 12
Hence, the value of n is 12 .
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Steps to solve y=3x + 8
What is the domain of y = sec(x)?
The domain of y = sec(x) is all real numbers except for values where the cosine function is zero.
Explanation:The domain of y = sec(x) is all real numbers except for values where the cosine function is equal to zero. Since the secant function is the reciprocal of cosine, it is undefined when cosine is zero.
So, the domain of y = sec(x) is all real numbers except for values of x where cos(x) = 0.
For example, if we consider the unit circle, the cosine function is equal to zero at π/2 and 3π/2. Therefore, the domain of y = sec(x) would exclude these values.
The domain of [tex]\( y = \sec(x) \)[/tex] is all real numbers except [tex]\( x = \frac{\pi}{2} + \pi \cdot n \)[/tex], [tex]\( n \)[/tex] integer.
Let's find the domain of [tex]\( y = \sec(x) \)[/tex].
The secant function, [tex]\( \sec(x) \)[/tex], is defined as the reciprocal of the cosine function, [tex]\( \cos(x) \)[/tex]. So, [tex]\( \sec(x) = \frac{1}{\cos(x)} \).[/tex]
The cosine function is defined for all real numbers, except where the denominator becomes zero, because division by zero is undefined.
So, to find the domain of [tex]\( \sec(x) \)[/tex], we need to find where [tex]\( \cos(x) \)[/tex] is not zero.
The cosine function has a range between -1 and 1. It equals zero at [tex]\( x = \frac{\pi}{2} + \pi \cdot n \)[/tex] and [tex]\( x = -\frac{\pi}{2} + \pi \cdot n \)[/tex], where [tex]\( n \)[/tex] is an integer.
So, the domain of [tex]\( \sec(x) \)[/tex] is all real numbers except where [tex]\( \cos(x) = 0 \)[/tex]. Therefore, the domain of [tex]\( \sec(x) \)[/tex] is [tex]\( x \neq \frac{\pi}{2} + \pi \cdot n \)[/tex] and [tex]\( x \neq -\frac{\pi}{2} + \pi \cdot n \)[/tex], where [tex]\( n \)[/tex] is an integer.
In interval notation, the domain of [tex]\( \sec(x) \)[/tex] is:
[tex]\[ (-\infty, -\frac{\pi}{2}) \cup (-\frac{\pi}{2}, \frac{\pi}{2}) \cup (\frac{\pi}{2}, \infty) \][/tex]
Write an appropriate inverse variation equation if y = 9 when x = 3.
FIND THE FOLLOWING USING THE GIVEN TRIANGLE...PLEASE HELP ME SUCK AT MATH...SOS!!! ASAP!!!!
perimeter = 20 +20 +24 = 64 feet
area = 12^2 + x^2 = 20^2
144 + x^2 = 400
x^2 = 256
x = sqrt(256) = 16 feet
area = 1/2 x 16 x 24 = 192 square feet
cost = 192 x $2 = $384
Choose the solution for the equation.
d3=284? need help asap
Answer:
the answer is A
Step-by-step explanation:
ttm