Answer:
t = 12
Step by step explanation:
(t + 6)(t - 8) = 72
t² - 8t + 6t - 48 = 0
t² - 2t - 120 = 0
(t + 10)(t - 12) = 0
t + 10 = 0 OR t - 12 = 0
t = -10 OR t = 12
(reject)
K
Choose the measurement closest to 30 km: 10 mi, 20 mi or 30 mi.
Choose the correct answer below.
20 mi
30 mi
10 Ini
O
O
O 10
Answer:
20 miles
Step-by-step explanation:
1.6km is equivalent to 1 mile
so 30km / 1.6 = 18.75 miles
therefore 20 miles is the closest to 30km
You are on a safari and pass by some hippos and birds (the kind
that hang out on top of the hippos). You see a total of 42 animals ane
114 legs. how many of each animal were there?
Answer:
15 hippos27 birdsStep-by-step explanation:
You have a total of 114 legs among hippos and birds, of which there are a total of 42. You want the number of each kind of animal.
SetupLet h represent the number of hippos. Then 42-h is the number of birds, and the total number of legs is ...
4h +2(42 -h) = 114
SolutionSimplifying the equation gives ...
2h +84 = 114
2h = 30 . . . . . . subtract 84
h = 15 . . . . . . . . number of hippos
42 -h = 27 . . . . number of birds
There were 15 hippos and 27 birds.
There are 10 applicants applying for 3 positions Hostess server and busier how many ways
The number of ways to select 3 position out of 10 applicant is 120 ways
What is combination?Combinations implies the selection of things from a given set of things. In this case, we intend to select the objects. Combination formula is illustrated as:
nCr = n! / ((n – r)! r!)
n = the number of items.
r = how many items are taken at a time.
Since there are 10 applicants applying for 3 positions. This will be:
= 10! / (10 - 3)!3!
= 10! / 7!3!
= 10 × 9 × 8 / 3 × 2
= 120
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What is the expected change in the dividend of a 6% preferred stock if the required rate of return drops instantly from 8% to 6%?
The expected change in the dividend of a 6% preferred stock is $75.
Given that, the required rate of return drops instantly from 8% to 6%.
What is the return?A return, also known as a financial return, in its simplest terms, is the money made or lost on an investment over some period of time.
The value of preferred stock = $100
Annual dividend = 100 × 6% = $6
Price of preferred stock when required return is 8% = Annual dividend / Required rate of return
= 6/8%
= 6 ×100/8
= $75
Therefore, the expected change in the dividend of a 6% preferred stock is $75.
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The kitchen is a square and has an area of 169 square feet.whatis the length of one side of Tito’s kitchen?
The length of one sides of the square Tito's Kitchen is 13 feet.
How to find the length of a square?A square is a quadrilateral with 4 sides equal to each other. The opposite sides of a square is parallel to each other.
The sum of angles in a square is 360 degrees. Each angle is 90 degrees.
The kitchen is a square and has an area of 169 square feet.
The length of one side of the kitchen can be calculated as follows:
area of the square kitchen = l²
where
l = side lengthTherefore,
area of the square kitchen = 169 ft²
169 = l²
square both sides of the equation
√169 = √l²
l = 13 ft
Therefore,
length of the square kitchen = 13 feet.
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A cube shaped aquarium with a side length of 1.2 meters is full of liquid. A fish swims in the container. What is the probability that the fish is at most 0.5 meters away from the center of the container?
The probability that the fish is at most 0.5 meters away from the center of the container, considering the volume of the cube, is given as follows:
0.0723 = 7.23%.
What is the volume of a cube?The volume of a cube of side length s is given by the side length cubed, that is:
V = s³.
The cube in this problem has a side length of 1.2 meters, hence the volume is given as follows:
V = 1.2³ = 1.728 cubic meters.
Considering only the inner 0.5 meters of the cube, the volume is given as follows:
V = 0.5³ = 0.125 cubic meters.
A probability is given by the division of the number of desired outcomes by the number of total outcomes, hence:
p = 0.125/1.728 = 0.0723 = 7.23%.
(desired volume is of 0.125 m³, total is of 1.728 m³).
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Quincy has a jewelry business in which he designs and sells bracelets. His daily profit, Q(x), can be modeled by the function Q(x) = 8.25x − 24.75, where x is the number of bracelets he sells. What is the value of Q(3), and what is its interpretation?
Q(3) = 0; If Quincy sells 3 bracelets, he will earn $0.
Q(3) = 0; If Quincy sells 0 bracelets, he will earn $3.
Q(3) = 3.36; If Quincy sells 3 bracelets, he will earn $3.36.
Q(3) = 3.36; If Quincy sells 3.36 bracelets, he will earn $3.
The correct interpretation is Q(3) = 0; If Quincy sells 3 bracelets, he will earn $0.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Q(x) = 8.25x − 24.75, where x is the number of bracelets he sells.
So, for x= 3 them Q(3)
Q(3)= 8.25 (3) - 24.75
Q(3) = 24.75 - 24.75
Q(3) = 0
Hence, Q(3) = 0; If Quincy sells 3 bracelets, he will earn $0.
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Mexico City had an estimated population of 18,066,000 people while Tokyo had an estimated population of 34,450,000 people. What was their combined population?
Answer:
Scientific notation: 5.2516 x [tex]10^{7}[/tex]
Standard notation 52,516,000
Step-by-step explanation:
Are you asking for the answer to be in scientific notation?
5.2516 x [tex]10^{7}[/tex] or 52,516,000
(1.8066 x [tex]10^{7}[/tex]) + (3.445 x [tex]10^{7}[/tex])
(1.8066 + 3.445) x [tex]10^{7}[/tex]
5.2516 x [tex]10^{7}[/tex]
The probability that a vehicle entering the Lu-
ray Caverns has Canadian license plates is 0.12; the
probability that it is a camper is 0.28; and the proba-
bility that it is a camper with Canadian license plates
is 0.09. What is the probability that
The conditional probability that a camper entering the Luray Caverns has Canadian license Plates is given by:
0.3214 = 32.14%.
What is Conditional Probability?Conditional probability is the probability of one event happening, considering the outcome of a previous event. The formula is given by the rule presented as follows:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
The probabilities that compose the formula are listed as follows:
P(B|A) is the probability of the event B happening, given that the event A has already happened.[tex]P(A \cap B)[/tex] is the probability of both the events, A and B, happening.P(A) is the probability of the event A happening.The events in this problem are given as follows:
Event A: Camper.Event B: Canadian license plates.The probabilities are given as follows:
P(A) = 0.28, P(A and B) = 0.09.
Hence the conditional probability is obtained as follows:
P(B|A) = P(A and B)/P(A) = 0.09/0.28 = 0.3214 = 32.14%.
Missing InformationThe probability asked is that a camper entering the Luray Caverns has Canadian license Plates.
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Multiply the difference of 10 and 8 by 4 expression
The Mathematical Expression formed is 4(10-8)
What is a Mathematical Expression?
In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations.
Solution:
The mathematical expression formed frrom the statement;
Multiply the difference of 10 and 8 by 4
is as follows,
4(10-8)
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A math class has a total of 33 students. The number of males is 15 more than the number of females. How many males and how many females are in the class?
Which values of a b and c correctly represent the answer in simplest form 3 1/4 divided by 2 3/8 equals a b/c. ( PLEASE HURYYYYY)
Answer:
Step-by-step explanation:
1. Put the words into math
3 3 1/4 divided by 2 3/8 equals a b/c.= 3 1/4/2 3/8
3 1/4/2 3/8=
1 7/19
2. Answer: 1 7/19
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y=2/3x-18 rate of change
The rate of change of the equation, y = 2/3x - 18, is: 2/3.
How to Determine the Rate of Change of a Linear Equation?The rate of change of a linear equation that is expressed in slope-intercept form as y = mx + b is represented by the value of m in the equation. It is also referred to as the slope of the equation.
For example, if we are given the equation, y = 4x + 5, the value of m is 4. This implies that the rate of change, which is the slope, is equal to 4.
In the same vein, we are given the equation, y = 2/3x - 18.
The value of m, which is the slope or rate of change in the equation y = 2/3x - 18 is equal to 2/3.
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calculate the length of a scarf with sections if each section is 1/2 foot long
Answer:
depends on how many sections there are
Step-by-step explanation:
if there were 2 then it would be one foot 4 sections equal 2 and so on. the ratio for this 2:1 meaning there has to be 2 sections for there to be one foot.
Describe the features of the function that can be easily seen when a quadratic function is given
in the form: y= A(x−A )( x− B) and how they can be identified from the equation.
The features of the functions when a quadratic function is given in the form: y = a (x − p) (x − q)
y = value in the y coordinates
a = constant in the equation
p and q = zeros or roots
x = value in the x coordinates
How to identify features in the equationWhen quadratic equation is written of the form y = a (x − p) (x − q), it is called the factored form of quadratic equation
The other form is ax^2 + bx + c and called standard form of quadratic equation
a in both cases are same and it helps to da if the curve opens upward or downward
when a is positive the curve opens upward but when it is negative the curve opens downward
Expanding the factored form of quadratic equation brings the equation to the standard form
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f(x) = √3x
g(x) = 3x + 2
Find (4) (2). Include any restrictions on the domain.
Option A is correct. The value of function (f/g)(x) is found to be [tex]\sqrt[3]{3x}[/tex]/(3x+2) where the condition is that x ≠ -2/3.
What exactly is a function composition?In mathematics, function composition is an operation in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.
What is the sum of two functions?The new function obtained by performing f first and then g is the combination of two functions g and f.
Given:
f(x) = [tex]\sqrt[3]{3x}[/tex]
g(x) = 3x + 2
(f/g)(x) = [tex]\sqrt[3]{3x}[/tex]/(3x+2)
Also, the denominator should not be equal to 0.
So, 3x + 2 ≠ 0
x ≠ -2/3
Therefore, the value of function is found to be [tex]\sqrt[3]{3x}[/tex]/(3x+2) where the condition is that x ≠ -2/3. So, Option A is correct
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Calculate the simple interest and maturity value
The simple interest is $420 and the maturity value is $$6,720
How to find the simple interest?Using this formula to find the simple interest
Simple interest = Principal × Interest rate × Time
Where:
Principal = $6300
Interest rate =4% or 0.04
Time = 20 month = 20/12 = 1.6666666
Let plug in the formula
Simple interest = $6,300 × 0.04 × 1.6666666
Simple interest = $420
Using this formula to find the maturity value
Maturity value = Principal + Interest
Maturity value = $6,300 + $420
Maturity value = $6,720
Therefore the interest is $420.
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a notebook manufacturer expectations fixed monthly costs of $46and variables costs of $1.50 per notebook produced.The notebooks are then sold for $3.50.
Answer: 13
Step-by-step explanation:
14 11/12 + 3 1/6 need help
Answer:
18.0833333333
Step-by-step explanation:
online calculator
Hey can someone please help me out? Thank you so much!
Answer:
Step-by-step explanation:
area=10×5+[(15-5)+7]/2×(10-6)
=50+(17)/2×4
=50+34
=?
what is the vaule of 2 × 4^2 + 5 enter the answer in the box
The value of the expression 2 x 4² + 5 will be 37
What is expression in mathematics?An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.
Given is the following expression -
2 x 4² + 5
On solving the expression, we get -
2 x 4² + 5
2 x 4 x 4 + 5
32 + 5
37
The value of the expression 2 x 4² + 5 will be 37
Therefore, the value of the expression 2 x 4² + 5 will be 37
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Square plank of 48 inches triangular base length of 12 inches height of 6 inches how much paper to cover
Applying the area of square and triangle, the amount of paper needed is: 180 inches².
What is the Area of a Square Shape and Area of a Triangular Shape?The area of a square shape = (side length of the shape)².
The area of a triangular shape = 1/2(base)(height)
The diagram that illustrates the problem given is shown in the image attached below, where the triangular paper to cover the triangular plank and the square paper for the square plank are shown also with their dimensions.
Therefore, the amount of paper that would cover the piece of art = area of the square shape + area of the triangular shape.
Area of the square shape = 12² = 144 inches²
Area of the square shape = 144 inches²
Area of the triangular shape = 1/2(12)(6)
Area of the triangular shape = 36 inches²
Amount of paper needed = 36 + 144
Amount of paper needed = 180 inches²
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Complete Question:
Theresa created a piece of art by attaching a square plank to a triangular plank. The square plank has a perimeter of 48 inches. The triangular plank has a base length of 12 inches and a height of 6 inches. She wants to cover the piece of art with colored paper.
How many square inches of paper are needed to cover Theresa's art piece?
find the 73rd term of the following arithmetic sequence 18,22,26,30
The arithmetic sequence has the 73rd term of 306
How to find the 73rd term for the arithmetic sequence?The sequence is given as:
18,22,26,30,....
The above sequence has the following parameters
First term, a = 18Common difference, d = 4 i.e. 22 - 18 = 4Number of terms , n = 73This means that the sequence is an arithmetic sequence
The nth term of an arithmetic sequence is calculated as
f(n) = a + (n - 1) * d
Substitute the known values in the above equation
So, we have the following equation
f(73) = 18 + (73 - 1) * 4
Evaluate
f(73) = 306
Hence, the 73rd term for the arithmetic sequence is 306
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Desmond is training for a bike race and is attempting to improve his average speed. With his old trainer, Desmond averaged a pace of 24 MPH. With his new trainer, he rode at an average speed of 30 MPH. By what percent did his average speed increase? %
The percent that Desmond average speed increase is 25%.
How to calculate the percentage?From the information, with his old trainer, Desmond averaged a pace of 24 MPH and with his new trainer, he rode at an average speed of 30 MPH.
It should be noted that the percentage increase in speed will be:
= Change in speed / Initial speed × 100
= (30 - 24) / 24 × 100
= 6/24 × 100
= 25%
The percentage is 25%.
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If you buy stock for $36.20 per share and sell that stock for $37.90 per share, what was your
return on investment?
Answer:
$1.70 per share
Step-by-step explanation:
37.90-36.20=1.70
2.) lee has seven 5-dollar bills and le quarters
in his pocket. How much money would he have
left in his pocket if he buyes a leather jacket
worth $35.20.
Amount of money left in Lee pocket after he buys a $35.20 leather jacket from the given amount is equal to $1.3.
As given in the question,
Conversion of quarter into dollars is :
1 quarter = 0.25 dollars
Amount of money with Lee in his pocket is equal to :
= ( 7 × 5) dollars + ( 6 × 0.25) dollars
= (35 +1.5) dollars
=$ 36.5
Cost of leather jacket buy by Lee = $35.20
Amount of money left in lee's pockets after purchasing jacket
= $( 36.5 - 35.20)
= $ 1.3
Therefore, amount of money left in Lee pocket after he buys a $35.20 leather jacket from the given amount is equal to $1.3.
The complete question is :
Lee has seven 5-dollar bills and 6 quarters in his pocket. How much money would he have left in his pocket if he buys a leather jacket
worth $35.20?
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i need help with this pls
Option C: The relationship between the statement cannot be determined.
What is Conditional statement?
Two independent statements can be related to each other in a logic structure called a conditional statement.
The first statement is presented with “if,” and is referred to as the hypothesis.
The second statement is linked with “then”, and is known as the conclusion.
The notation associated with conditional statements typically uses the variable p for the hypothesis statement, and q for the conclusion.
p → q
Explanation for the answer:
The converse statement is notated as q→p (if q, then p). The original statements switch positions in the original “if-then” statement.The inverse statement assumes the opposite of each of the original statements and is notated ∼p→∼q (if not p, then not q).The contrapositive statement is a combination of the previous two. The positions of p and q of the original statement are switched, and then the opposite of each is considered: ∼q→∼p (if not q, then not p).
So, from the above we can clearly see that the both the statement 1 and statement are not start with "if" and "then".
Therefore, their relationship cannot be determined.
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The measure of an obtuse angle is A: greater than 0 and less than 90 degrees B: 90 degrees C. greater than 90 and less than 180 degrees
The measure of an obtuse angle is greater than 90° but less than 180°
What is an obtuse angle?An obtuse angle is a type of angle that is always larger than 90° but less than 180°. In other words, it lies between 90° and 180°.
An angle is the space between two intersecting lines or surfaces at or close to the point where they meet.
Angles are mostly measured in degrees. But it can also be measured in radian. Examples of obtuse angle are 91°, 100°, 150° e.t.c
Other examples of angles are acute angle, reflex angle , right angle.
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What is the value of csc 47° to the nearest thousandth?
Answer: 1.367
Step-by-step explanation:
csc47° = 1.3673 ≈ 1.367
The value of cosec 47° is 1.367.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
cosec 47°
The value of cosec 47°.
= 1.367334
Rounding to the nearest thousandth.
= 1.367
Thus,
The value of cosec 47° is 1.367.
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