The weight of a newly hatched channel catfish after four weeks of exponential growth is approximately 1.14 grams.
Explanation:To find the weight at the end of four weeks, we need to convert the number of weeks to days since the growth rate is given in terms of daily percentage increase. The formula to calculate exponential growth is A = C(1 + r)^t, where A is the final weight, C is the initial weight, r is the growth rate, and t is the number of periods. In this case, C = 0.3 grams, r = 0.10 (10% daily increase), and t = 4 weeks x 7 days/week = 28 days. Plugging in these values, we get A = 0.3(1 + 0.10)^28. Evaluating the expression, the weight at the end of four weeks is approximately 1.14 grams.
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Angles α and β are the two acute angles in a right triangle. Use the relationship between sine and cosine to find the value of α if α < β. sin(2x − 8) = cos(6x − 6)
Answer:
The value of angle α is 18 degree.
Step-by-step explanation:
Given information: Angles α and β are the two acute angles , α < β.
Given equation is
[tex]\sin (2x-8)=\cos (6x-6)[/tex]
[tex]\cos (90-(2x-8))=\cos (6x-6)[/tex] [tex][\because \sin (90-x)=\cos x][/tex]
Equating both sides.
[tex]90-2x+8=6x-6[/tex]
[tex]98+6=6x+2x[/tex]
[tex]104=8x[/tex]
[tex]13=x[/tex]
The value of x is 13.
The measure of angles is
[tex]2x-8=2(13)-8=18[/tex]
[tex]6x-6=6(13)-6=72[/tex]
Since 18<72, therefore the value of angle α is 18 degree.
Answer:
A
Step-by-step explanation:
Which pair of numbers are not opposites? Select one: a. |7| and -7 b. 72 and -72 c. 27 and |-27| d. 27 and -27
Find the area of the entire slice of pizza. Since the slice of pizza is part of a whole pie, let’s think of the pizza as a sector of a circle. Calculate the area. Be sure to show all of you work.
Answer:
The area of the entire slice of pizza = 14.13 square inches
Step-by-step explanation:
From the given figure of pizza.
The radius of the pizza is 6 in.
Central angle = 45°
The pizza is in the shape of the circle. We need to find the entire slice of pizza.
Here we have to use the formula to find the area of sector of a circle.
Area of a sector of a circle = [tex]\frac{Central angle}{360} *\pi *r^2[/tex]
Now plug in central angle = 45, r = 6 in the above formula to find the area of the slice of the pizza.
The area of the entire slice of pizza = [tex]\frac{45}{360} *3.14*6^2[/tex]
The value of π = 3.14
= [tex]\frac{45}{360} *3.14*36[/tex]
Simplifying, we get
= [tex]\frac{45}{10} *3.14[/tex]
= 141.3/10
The area of the entire slice of pizza = 14.13 square inches
Which expression is another way to show 9/2
The expression 9/2 can be equivalently expressed as the mixed number 4 1/2, or by multiplying the numerator and denominator by the same number, such as 18/4.
Explanation:The question asks for an expression that is equivalent to 9/2. One way to express this fraction differently is by converting it into a mixed number. Since 9 divided by 2 is 4 with a remainder of 1, we can express 9/2 as 4 1/2 (four and a half). Another method is to multiply both the numerator and the denominator by the same number, which does not change the value of the fraction.
For example, multiplying both by 2 gives us 18/4, which is equivalent to 9/2. Multiplying or dividing both the numerator and denominator by the same non-zero number is a skill that can provide equivalent fractions.
A basketball is theown upwards. The height F(t), The height in feet, in time, t, in seconds is goven by the following. f(t)= -16t(2) +44+ 12. Which of the following is a reasonable domain of the graphof the function when the basketball falls from ots maximum height to the ground?
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2. A cube-shaped aquarium has edges that are 3 ft long. The aquarium is filled with water that has a density of 62 lb/ft^3
(a) Should the aquarium be placed on a table that can support a maximum weight of 200 lb? Explain why or why not.
(b) Would the density of the water change if the aquarium was only half full? Explain.
What’s the answer to question 13
The diagonal of a TV screen is 26 inches. The screen is 18.8 inches wide. How high is the screen? Round to the nearest hundredths place.
The height of the TV for the condition is 17.96 inches.
What is Pythagoras' theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.
Given the diagonal of the TV = 26 inches
width of screen = 18.8 inches
let the shape of TV be rectangular
so diagonal divide the rectangle in right triangles,
by Pythagoras' theorem we can find the height,
h² = b² + h²
h = hypotenuse = diagonal for given = 26 inches
b = base = width = 18.8 inches
h = height
(26)² = (18.8)² + h²
h² = 676 - 353.44
h = √322.56
h = 17.96 inches
Hence the height of TV is 17.96 inches.
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A total of 705 tickets were sold for the school play. they were either adult tickets or student tickets. there were 55 more student tickets sold than adult tickets. how many adult tickets were sold?
There were 380 student tickets and 325 adult tickets were sold for the school play.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let the number of student tickets would be x and the number of adult tickets would be y
As per the given question, the following system of equations:
x - y = 55 ....(i)
x + y = 705 ....(ii)
Add both equations,
x - y + x + y = 55 + 705
2x = 760
x = 760 / 2
x = 380
Substitute the value of x = 380 in equation (ii),
x + y = 705
380 + y = 705
y = 705 - 380
y = 325
Hence, there were 380 student tickets and 325 adult tickets were sold for the school play.
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Which graph shows a plot of the complex number i - 2
A classroom of children has 16 boys and 19 girls in which five students are chosen to do presentations. what is the probability that at least four boys are chosen?
The probability of at least four boys from five selected students depends on the ratio of the favorable outcomes (either four boys and one girl, or all five are boys) to the total combinations of five students from 35, calculated using Combinatorics.
Explanation:The subject of your question is Probability, which falls under Mathematics. The question can be approached through Combinatorics, a branch of Mathematics that deals with combinations of objects belonging to a finite set following certain constraints.
To address your question, we first need to find the total number of ways that five students can be selected from the total 35 (16 boys and 19 girls). This can be calculated using combinations, denoted as C(n, r), where n is the total number of elements and r is the number of elements to choose from the total. In this case, the total combinations would be C(35, 5).
Next, we need to find the combinations where at least four boys are chosen. This could mean either four boys and one girl are chosen, or all five chosen are boys.
For the situation where four boys and one girl are chosen, the possible combinations would be C(16, 4) * C(19, 1). For the situation where all chosen are boys, the possible combinations would be C(16, 5).
So, the total desired combinations would be C(16, 4)*C(19, 1) + C(16, 5).
The probability of choosing at least four boys would be the ratio of desired combinations to the total combinations. Thus, Probability = [C(16, 4)*C(19, 1) + C(16, 5)] / C(35, 5).
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A ball is dropped from a height of 12 feet. Each time it bounces, it rebounds 3
4
of the distance it has fallen. How far will it rebound after the third bounce?
A) 0.75 feet
B) 5.0625 feet
C) 6.75 feet
D) 9 feet
Final answer:
After calculating the rebound height for each bounce by multiplying the height from the previous bounce by 75%, the ball will rebound to a height of B) 5.0625 feet after the third bounce.
Explanation:
The question is asking how far the ball will rebound after the third bounce. Initially, the ball is dropped from a height of 12 feet. On each bounce, it rebounds to ⅔3 (75%) of the previous height. To solve this, we need to calculate the height achieved on each successive bounce.
First bounce: 12 feet * ⅔3 = 9 feet
Second bounce: 9 feet * ⅔3 = 6.75 feet
Third bounce: 6.75 feet * ⅔3 = 5.0625 feet
Therefore, after the third bounce, the ball will rebound to a height of 5.0625 feet, which corresponds to option B.
What is the value of y?
I think the hypotenuse is 8 and if it is, am I supposed to do
C^2 - B^2 = A^2?
A movie theater is 3 blocks due north of a supermarket and a beauty parlor is 4 blocks due east of the movie theater. how many blocks long is the nearest street that runs directly from the supermarket to the beauty parlor?
The dot product of u with itself is 24. what is the magnitude of u?
Answer - u = 4.8989
u ^ 2 = 24
u = sqrt (24)
u = 4.8989
Answer:
[tex]2\sqrt6[/tex]
Step-by-step explanation:
We have been given that the dot product if u with itself is 24.
Now, we know that the dot product of vector a and b is given by
[tex]a\cdot b=|a||b|\cos\theta[/tex]
Here, [tex]\theta[/tex] is the angle between the vectors a and b.
We have to find the dot product of u with itself. Hence,
a = u
b = u
[tex]\theta=0[/tex]
Thus, dot product is given by
[tex]u\cdot u=|u||u|\cos0\\\\24=|u||u|\cdot1\\\\|u|^2=24\\\\|u|=2\sqrt6[/tex]
Thus, the magnitude of u is [tex]2\sqrt6[/tex]
Is this function one-to-one? Explain how you determine your answer
What is true about side AB and side AD?
1) The slopes are the same.
2)The slopes are the opposite reciprocal.
If you work 52 weeks/year and 40 hours/week, how many hours would you work in one year?
All of the following represent the same expression except _____.
-8ab
-8(a)(b)
8 - ab
-8 · a · b
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The expression that is not the same as the rest of the expressions is
8 - ab.
Option C is the answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example:
2 + 3x + 4y = 7 is an expression.
3x - 5 is an expression.
4x + 4 is an expression.
4 x 5 - 5x is an expression.
We have,
1) -8ab
2) -8 (a) (b)
= -8ab
3) 8 - ab
4) -8.a.b
= -8ab
We see that,
All the expressions are the same except the expression
8 - ab
Thus,
The expression that is not same with the rest of the expression is
8 - ab.
Option C is the answer.
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Keisha can jog 2 miles in 24 minutes. At the same rate , how many miles can she jog in 60 minute
Is (3, 2) a solution to this system of equations?
8x + 7y = 37
2y = 4x - 2
The Menswear Department of Nancy‘s Department Store had sales of $191,000, cost of goods sold of $134,000, indirect expenses of $13,550, and direct expenses of $27,800 for the current period. What is the Menswear Department's contribution to overhead as a percent of sales?
To calculate the overhead contribution, divide the indirect expenses by the total sales, and multiply by 100. The Menswear Department's contribution to overhead as a percent of sales for this period is approximately 7.09%.
Explanation:The student is asking about calculating the overhead contribution rate. Overhead contribution can be calculated by dividing indirect expenses by total sales and multiplying by 100. In this case, total sales for the Menswear Department are $191,000 and indirect expenses are $13,550.
Therefore, the rate is calculated as follows: ($13,550 / $191,000) * 100 = 7.09%. Thus, the Menswear Department's contribution to overhead as a percent of sales is 7.09%.
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Solve x2 + 10x + 12 = 36 for x. x = â12 or x = 2 x = â11 or x = 1 x = â2 or x = 12 x = â1 or x = 11
57(1.31)^t interpret the meaning of the expression
A. The initial number of bacteria is 57 and the growth rate is 3.1% per hour
B. The initial number of bacteria is 57 and the growth rate is 31% per hour
C.the initial number of bacteria is 131 and the growth rate is 5.7% per hour
D.the initial number of bacteria is 131 and the growth rate is 57% per hour
B. The initial number of bacteria is 57 and the growth rate is 31% per hour
57 is the initial all by itself and 31 is the growth rate. Don't really know why and how to explain the Percentage application but I got the answer correct on my test so.................................
What is the value of b?
Round your answer to the nearest tenth.
15.7 yd
24.1 yd
35.1 yd
36.2 yd
The figure shows acute triangle A B C. The measure of angle B is 34 degrees. The length of side A B is 28 yard. The length of side B C is 22 yard. The length of side C A is b.
Answer:
A. 15.7 yards.
Step-by-step explanation:
Please find the attached file.
We have been given that in triangle ABC, the measure of angle B is 34 degrees. The length of side AB is 28 yards and the length of side BC is 22 yards. The length of side CA is b.
We will use law of cosines to find the length of side 'b'.
[tex]c^2=a^2+b^2-2ab\times cos(C)[/tex]
Upon substituting our given values in above formula we will get,
[tex]CA^2=22^2+28^2-2\times 22\times 28\times cos(34^{\circ})[/tex]
[tex]CA^2=484+784-1232\times 0.829037572555[/tex]
[tex]CA^2=1268-1021.37428938776[/tex]
[tex]CA^2=246.62571061224[/tex]
Taking square root of both sides we will get,
[tex]CA=\sqrt{246.62571061224}[/tex]
[tex]CA=15.70432139929\approx 15.7[/tex]
Since the length of side CA is b, therefore, the value of b is 15.7 yards and option A is the correct choice.
Today, 32 customers at Tasha's Juice Emporium bought a total of 512 ounces of juice. How much juice did each customer buy on average?
The amount of juice did each customer buy on average is,
⇒ 16 ounces
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
Today, 32 customers at Tasha's Juice Emporium bought a total of 512 ounces of juice.
Hence, The amount of juice did each customer buy on average is,
⇒ 512 / 32
⇒ 16 ounces
Thus, The amount of juice did each customer buy on average is,
⇒ 16 ounces
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A barn is an atomic unit of area equal to 10–28 m2. what is the surface area of the earth expressed in units of barn? assume the earth is a sphere with a radius of km. (the surface area of a sphere is 4πr2.)
Can someone help me find the area of the following figure
Write the sum using summation notation, assuming the suggested pattern continues.
-8 - 3 + 2 + 7 + ... + 67
Remark: L = a + (n - 1)d is your starting point. In order to find the sum, you must know the value of n.
Givens: a = - 8; d=5; L = 67
Substitute and solve
67 = - 8 + (n - 1)*5 Add 8 to both sides.
67 + 8 = -8 + 8 + (n - 1)*5
75 = (n - 1)*5 Divide by 5 on both sides.
15 = n - 1 Add one to get the answer.
16 = n
Part Two: Use The summation notation to find the sum. Unfortunately, I don't know how to do this in latex.
Sum (n = 1 to 16) -8 + 5*(n - 1)
If x varies directly as y, and x = 48 when y = 16, find x when y = 5.
A) 5/3
B) 153.6
C) 15