Answers
Related Questions
how to Solve for the Missing Side
Answers
Remember SOHCAHTOA
You need to find the hypotenuse, and you are given the opposite side to the given angle. Which means you will be solving Sine.
Now just plug the numbers in.
[tex]Sin 67 = \frac{15}{x} \\Sin 67 (x) = 15 \\\frac{sin67(x)}{sin 67} = \frac{15}{sin67} \\x = 16.2954[/tex]
Atrap and Bracken are two rival insurance companies. Atrap and Bracken have premiums of $150 and $100 and deductibles of $2,500 and $3,500 respectively. The average expense of surgery is $25,000. If after 5 years, 25 of the 1,000 people registered with Bracken have gone through surgery, where does Bracken stand in terms of gains or losses?
Answers
Answer:
Bracken has incurred a loss of $37,500
Step-by-step explanation:
People who have registered with Bracken insurance company pays premium of $100. 1,000 people in total have registered with Bracken. In 5 years Bracken would have earned an income of $500,000 [tex]\left ( $100\times1,000\times5)\right[/tex].
25 among the 1,000 registered have undergone surgery. Average surgery expense is $25,000. $3,500 is deductible. So Bracken's total expense per client is $21,500 (25,000 - 3,500). For 25 patients, it will be $537,500 [tex]($21,500\times25)[/tex].
Since expenses of $537,500 is more than income of $500,000, Bracken incurs a loss of $37,500 (500,000 - 537,500) over 5 years.
Therefore, Bracken's loss over 5 years is $37,500
What is the area of this composite figure? 12ft2 80 ft2 88 ft2 100 ft2
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[tex]x=10ft-2ft=8tf\\\\A_1=10ft\cdot8ft=80ft^2\\\\y=10ft-6ft=4ft\\\\A_2=4ft\cdot2ft=8ft^2\\\\A_F=A_1+A_2\to A_F=80ft^2+8ft^2=88ft^2[/tex]
[tex]Answer:\ \boxed{88ft^2}[/tex]
A ball is launched into the sky at 272 feet per second from the roof of a skyscraper 1,344 feet tall. The equation for the ball’s height h at time t seconds is h = -16t2 + 272t + 1344. When will the ball strike the ground?
Answers
Answer:
Time taken to reach the ball to the ground is 21 seconds.
Step-by-step explanation:
Given : A ball is launched into the sky at 272 feet per second from the roof of a skyscraper 1,344 feet tall. The equation for the ball’s height h at time t seconds is [tex]h = -16t^2 + 272t + 1344[/tex].
To find : When will the ball strike the ground?
Solution :
The equation for the ball's height 'h' at time 't' is given by,
[tex]h(t)= -16t^2 + 272t + 1344[/tex]
When the ball strike the ground the height of the ball became zero.
Substitute h=0 in the given equation,
[tex]-16t^2 + 272t + 1344=0[/tex]
Taking 16 common,
[tex]16(-t^2 + 17t + 84)=0[/tex]
or [tex]t^2-17t-84=0[/tex]
Solve by middle term split,
[tex]t^2-21+4t-84=0[/tex]
[tex]t(t-21)+4(t-21)=0[/tex]
[tex](t-21)(t+4)=0[/tex]
[tex]t=21,-4=0[/tex]
Reject t=-4 as time can never be negative.
Therefore, Time taken to reach the ball to the ground is 21 seconds.
Tangerine trees yield 50 pounds of fruit per acre and grapefruit trees yield 75 pounds of fruit per acre. Suppose Josh's farm has t acres of tangerine trees, g acres of grapefruit trees, and yields 1,500 pounds of citrus. What is the constraint equation that represents this scenario?
50t + 75g = 1,500 75t + 50g = 1,500 125c = 1,500 t + g = 1,500
Answers
Solution:
Tangerine trees = 50 pounds/acre, t acres
Grapefruit trees = 75 pounds/acre, g acres
Total weight of fruits possible = 1,500 = 50*t + 75*g
That is,
50t + 75g = 1,500
Therefore, the first option is correct.
Answer: 50t+75g=1,500
If f(x) = x^2 and g(x) = 1/2x + 3, find g(f(-1)).
A.) -1
B.) 1/25
C.) 1/5
D.) 1
Answers
x=-1→f(-1)=(-1)^2→f(-1)=1
g(x)=1/(2x+3)
g(f(-1))=g(1)→x=1→g(1)=1/[2(1)+3]=1/(2+3)→g(f(-1))=1/5
Answer: Option C.) 1/5
What number should be added on both sides of the equation to complete the square x2 -6x =5
Answers
Answer:
We should add 9 on the both sides of the given equation.
Step-by-step explanation:
Since, for making a perfect square on the left side of a quadratic equation,
We add the square of the half of the coefficient of x on both sides,
The given equation,
[tex]x^2-6x = 5[/tex]
Here, the coefficient of x is 6,
Half of 6 = 3
Square of 3 = 9,
Thus, we should add 9 on the both sides of the given equation.
Verification :
[tex]x^2 - 6x + 9 = 5 + 9[/tex]
[tex](x-3)^2 = 14[/tex]
hey can you please help me posted picture of question
Answers
N (k):
Where, the indepent variable is k
The dependent variable is N
For the function:
k (n):
the independent variable is n
The dependent variable is k
Thus,
N (12) = 4
k (4) = 12
Answer:
TRUE
option A
A pound of chocolate costs 7 dollars. Tiffany buys p pounds. Write the equation to represent the total cost c that Tiffany pays.
Answers
Final answer:
The equation to represent the total cost c that Tiffany pays for p pounds of chocolate, when a pound costs 7 dollars, is c = 7 × p. This is a simple linear equation with 7 as the price per pound.
Explanation:
The question asks to write an equation to represent the total cost c that Tiffany pays for p pounds of chocolate, with the knowledge that a pound of chocolate costs 7 dollars.
To find the total cost c, we simply need to multiply the cost per pound of chocolate by the number of pounds Tiffany buys. If each pound costs $7, then the equation showing the total cost for p pounds would be:
c = 7 × p
Where:
c represents the total cost
p represents the number of pounds of chocolate
This is a straightforward linear equation with the coefficient 7 representing the price per pound of chocolate.
According to the order of operations, which of the following should be evaluated first? exponents multiplication or division expressions within parentheses addition or subtraction
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expressions within parentheses
the correct answer is the expression with parentheses
What is the answer for 5 3/4+3 1/3 =?
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Let's start by adding the whole numbers.
5+3=8
Set it to the side.
Now let's rewrite the problem without the whole numbers.
[tex] \frac{3}{4} + \frac{1}{3} [/tex]
We must find the least common denominator.
The LCD is 12.
In order to get 12 we must multiply by 3 on the left and 4 on the right.
[tex] \frac{3*3}{4*3} + \frac{1*4}{3*4} [/tex]
[tex]\frac{9}{12} + \frac{4}{12} [/tex]
Now just add them together since they have a common denominator.
[tex] \frac{13}{12} [/tex]
Now we need to simplify
[tex]1 \frac{1}{12} [/tex]
Now it is time to add that 8 back
8+[tex] 1 \frac{1}{12} [/tex]
Add the whole numbers
8+1=9
Answer: [tex] 9 \frac{1}{12} [/tex]
In RST , RS=11 ,RT=9 and ST=6 which angle of RST has the smallest measure ?
Answers
C. ∠R
<R angle of RST has the smallest measure.
The correct option is C.
We have,
RS=11 ,RT=9 and ST=6
Now, from the given lengths it can be seen that the length of ST is shortest and length of RS is longest.
By the definition which states that,
The angle opposite to longest side is largest and the angle oppsite to shortest side is smallest.
From given, <R is opposite to shortest side ST.
Thus, the smallest angle is R.
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In the linear equation y = 2x + 1, if x increases by 4 points, how much will y increase?
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If [tex]\(x\)[/tex] increases by 4 points, [tex]\(y\)[/tex] will increase by 8 units.
In the linear equation [tex]\(y = 2x + 1\)[/tex], the coefficient of [tex]\(x\)[/tex] is 2. This means that the slope of the line is 2, and for every one unit increase in [tex]\(x\), \(y\)[/tex] will increase by 2 units.
Given that [tex]\(x\)[/tex] increases by 4 points, the corresponding increase in [tex]\(y\)[/tex] can be found by multiplying the change in [tex]\(x\)[/tex] by the slope:
[tex]\[\Delta y = \text{Slope} \times \Delta x\][/tex]
[tex]\[ \Delta y = 2 \times 4 = 8\][/tex]
Therefore, if [tex]\(x\)[/tex] increases by 4 points, [tex]\(y\)[/tex] will increase by 8 units.
Example:
Let's use the given linear equation [tex]\(y = 2x + 1\)[/tex] and demonstrate how an increase in [tex]\(x\)[/tex] by 4 points results in an increase in [tex]\(y\)[/tex] by 8 units.
Given Linear Equation:
[tex]\[y = 2x + 1\][/tex]
Let's consider an initial point on the line where [tex]\(x = 3\)[/tex]. Find the corresponding [tex]\(y\)[/tex]:
[tex]\[y = 2(3) + 1 = 7\][/tex]
So, when [tex]\(x = 3\), \(y = 7\)[/tex].
Now, if [tex]\(x\)[/tex] increases by 4 points, new [tex]\(x\)[/tex] value will be [tex]\(3 + 4 = 7\)[/tex].
Using the same linear equation to find the new [tex]\(y\)[/tex]:
[tex]\[y_{\text{new}} = 2(7) + 1 = 15\][/tex]
Now, calculate the increase in [tex]\(y\)[/tex]:
[tex]\[\Delta y = y_{\text{new}} - y_{\text{initial}} = 15 - 7 = 8\][/tex]
So, in this example, when [tex]\(x\)[/tex] increases by 4 points (from 3 to 7), [tex]\(y\)[/tex] increases by 8 units (from 7 to 15), confirming that the increase in [tex]\(y\)[/tex] is proportional to the increase in [tex]\(x\)[/tex] with a slope of 2.
Find the magnitude and direction (in degrees) of the vector. v = ‹ - sqrt(7)/9, - sqrt(2)/3 ›
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lvl = root ((- root (7) / 9) ^ 2 + (- root (2) / 3) ^ 2)
lvl = 0.555555556
The address is given by:
cos (theta) = (- root (7) / 9) / (0.555555556)
Clearing theta:
theta = acos ((- root (7) / 9) / (0.555555556))
theta = 121.95 degrees
Answer:
The magnitude and direction (in degrees) of the vector are:
lvl = 0.555555556
theta = 121.95 degrees
if you laid 9 bolts end-to-end that each measure seven eighths of an inch, how long would that row of bolts be?
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Starting time 7:43 elapsed time 36 min
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STEP 1:
Add the minutes together (not hours)
=43 + 36
=79 minutes
STEP 2:
1 hour= 60 minutes
since there are only 60 minutes in an hour, add one hour to 7 above and subtract 60 from step 1 to find remaining minutes
=79 - 60
=19 minutes
STEP 3:
add another hour to 7 since we have an extra 60 minutes
=(7 hours +1 hour) + 19 minutes
=8:19
ANSWER: 8:19 is the new time
Hope this helps! :)
I need help on this please
Answers
a(v)=√(3V/8)
The explanation is shown below:
To solve this problem you must apply the following proccedure:
1. You must use the formula for calculate the volume of a square pyramid, which is:
V=a²h/3
2. Therefore, when you clear a, you obtain:
3V=a²h
3V/h=a²
a=√(3V/h)
3. You have that heigth is 8, then:
a(v)=√(3V/8)
4. So, as you can see, the correct answer is the option mentioned above.
simple interest $4000 at 7% for 8 mo.
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I = (4000 x .07 x [tex] \frac{8}{12} [/tex]) + 4000
I = 186.67 + 4000
I = around $4186.67
*hope this helped!
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A wooden block in the shape of a rectangular prism is cut into two congruent pieces. Which statement best compares the surface areas of the pieces to the surface area of the original block?
A. The surface area of each piece is equal to 1/2 surface area of the original block.
B. The surface area of each piece is equal to the sum of half the surface area of the original block plus half the area of the face created by the cut.
C. The surface area of each piece is equal to the sum of half the surface area of the original block plus the area of the face created by the cut.
D. The surface area of each piece is equal to the surface area of the original block minus the area of the face created by the cut.
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The option c is correct
What is rectangular prism ?A rectangular prism is a polyhedron with two congruent and parallel bases. It is also called a cuboid. A rectangular prism has six faces, and all the faces are in a rectangle shape and have twelve edges. Because of its cross-section along the length, it is said to be a prism.
According to the question,
The surface area of each piece is equal to the sum of half the surface area of the original block plus the area of the face created by the cut.
Hence, option c is correct for given condition.
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hey can you please help me posted picture of question
Answers
(4 - 6i)(6 - 8i)
= 4(6-8i) - 6i(6-8i)
= 24 - 32i - 36i + 48i²
= 24 - 68i + 48(-1)
= 24 - 68i - 48
= - 24 - 68i
Find the intervals on which f is increasing and decreasing, find the local maximum and minimum values of f, find the intervals of cocavity and inflection f(x) 2x^3 + 3x^2 -36x
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Increasing: x ∈ (-∞, -3) ∪ (2, ∞)
Decreasing: x ∈ (-3, 2)
Local maximum: (-3, 81)
Local minimum: (2, -44)
Concave downward: x ∈ (-∞, -0.5)
Concave upward: x ∈ (-0.5, ∞)
Point of inflection: (-0.5, 18.5)
What is the total future value six years from now of $80 received in one year?
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Milt built a prism using a 3 unit cubes. He adds two more layers of 3 unit cubes each.how many unit cubes are used for the prism?
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1) Milt built a prism using a 3 unit cubes
total unit cubes is 3
2) He adds two more layers of 3 unit cubes each
total unit cubes=3+2*3----> 9 unit cubes
the answer is
9 units cubes
Milt used a total of 9 unit cubes to build his prism. This was calculated by multiplying the quantity of unit cubes in each layer (3 cubes) by the total number of layers (3).
Explanation:This is a Mathematics question about the concept of volume in prisms, specifically a cube. Milt starts by building a prism using 3 unit cubes and then adds 2 more layers of 3 unit cubes each. This means he has 3 layers of 3 cubes each.
We can calculate the total number of unit cubes used by multiplying the number of cubes in each layer by the number of layers. Here's the step-by-step calculation:
Start with quantity in a single layer: 3 unit cubes.
Multiply by the total number of layers to get the total quantity: 3 layers * 3 cubes/layer = 9 unit cubes.
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In 2012, the population of a city was 6.81 million. the exponential growth rate was 1.61% per year. a) find the exponential growth function. b) estimate the population of the city in 2018. c) when will the population of the city be 10 million? d) find the doubling time.
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y = A * (b) ^ t
Where,
A: initial amount
b: growth rate
t: time
For each of the questions we must make use of this equation in the following way:
Part A:
y = 6.81 * (1.0161) ^ t
Part B:
y = 6.81 * (1.0161) ^ 6
y = 7.49 million
Part C:
10 = 6.81 * (1.0161) ^ t
log1.0161 ((1.0161) ^ t) = log1.0161 ((10 / 6.81))
t = log1.0161 ((10 / 6.81))
t = 24.05 years
Part D:
2 * 6.81 = 6.81 * (1.0161) ^ t
log1.0161 ((1.0161) ^ t) = log1.0161 ((2 * 6.81 / 6.81))
t = log1.0161 (2)
t = 43.40 years
Which of the following represents the zeros of f(x) = 6x3 − 35x2 + 26x − 5?
the answer choices are
A. -5, one third, one half
B. 5, negative one third, one half
C. 5, one third, negative one half
D. 5, one third, one half
Answers
f(x)=6x³-35x²+26x-5
to get the zeros we need to factorize the polynomial given:
to factorize we look for a number such that when we substitute in the equation we get a zero:
first number is:
x=5
thus:
to get the rest of the number we shall have:
(6x³-35x²+26x-5)÷(x-5)
=(3x-1)(2x-1)
thus the other roots are:
x=1/3 and x=1/2
hence the answer will be:
C. 5, one third, negative one half
Write an equation to solve each problem and then solve it. There are two numbers whose sum is 53. Three times the smaller number is equal to 19 more than the larger number. What are the numbers?
Answers
x------> larger number
y------> smaller number
we know that
x+y=53------> y=53-x-----> equation 1
3y=x+19-----> equation 2
substitute equation 1 in equation 2
3*[53-x]=x+19------> 159-3x=x+19----> 3x+x=159-19-----> 4x=140
x=140/4-----> x=35
y=53-x----> 53-35-----> y=18
the numbers are
35 and 18
You roll a standard number cube. Find P(number is not 2).
Select one:
a. 2/3
b. 1/2
c. 5/6
d. 1/6
Answers
1,2,3,4,5,6
P, is any of those numbers that are not 2.
2 is one of the numbers in 6, and so it is 1/6 of the die.
6/6 - 1/6 = 5/6
C) 5/6 is your chance of getting a number that is not 2
hope this helps
At the end of the past month the cash account of a company had an ending balance of 6750. During the last month the account was debited for a total of 11350 and credited for a total of 10500. What was the balance in the cash account at the of the last month
Answers
6750 -11350 +10500 = 5900
At the end of last month, the cash account balance was 5900.
What is the inequality for this verbal description?Sam has d dollars to spend on grapes and carrots. He wants to buy one bag of grapes for $4.00 and c pounds of carrots that cost $2.00 per pound. Which inequality represents this situation?
Answers
this tells us that $4 for grapes plus c bags of carrots that are $2 per pound will give us his total. he wants this to be less than or equal to d.
if able please vote brainliest if you like my response! thanks
Final answer:
The inequality for Sam's expenditures on grapes and carrots, with grapes costing $4 and carrots costing $2 per pound, is 4 + 2c <= d.
Explanation:
The inequality that represents Sam's spending on grapes and carrots, given that he has d dollars to spend, is 4 + 2c ≤ d. This inequality is derived from the cost of one bag of grapes, which is $4, and the cost of carrots, which is $2 per pound. The variable c represents the number of pounds of carrots Sam wants to buy. The total cost of grapes and carrots must be less than or equal to the amount of money Sam has, which is d dollars.
the local weather forecast has been accurate for 17 of the past 33 days based on this fact what is the relative frequency probability that the forecast for tomorrow will be accurate
Answers
Answer: 17/33
[tex] \frac{17}{33} [/tex]