Answer:
see explanation
Step-by-step explanation:
The width w is 4 feet longer than two times the length , then
w = 2l + 4
The area (A) of the rectangle is length × width , then
A = l(2l + 4) ← distribute parenthesis
A = 2l² + 4l
Given A = 16
2l² + 4l = 16
Subtract 16 from both sides
2l² + 4l - 16 = 0 ( divide through by 2 )
l² + 2l - 8 = 0 ← in standard form
(l + 4)(l - 2) = 0 ← in factored form
Equate each factor to zero and solve for l
l + 4 = 0 ⇒ l = - 4
l - 2 = 0 ⇒ l = 2
However l > 0 then l = 2
and w = 2l + 4 = 2(2) + 4 = 4 + 4 = 8
The length of the rectangle is 2 feet and
the width is 8 feet
The zoo has 4 tigers and plans to adopt more tigers soon. Gabby meets with Chloe, the manager of the tiger exhibit, to discuss the tigers’ habitat. They want to make sure there is enough space for the new tigers.
The Natureland Zoo has these requirements for a tiger habitat:
The trees, feeding station, and drinking station need at least 300 square feet all together.
Each tiger needs at least 225 square feet of space.
How many square feet of space is the zoo required to have for 4 tigers? Show your work.
Answer:
multiple 4×225 because there are 4 tigers and one Tiger needs 225 square feet so mutiple 4×225 and you got 900 so the answer will be 900 square feet
4•4 - (-1)
Does this equal 3
Answer:
no, 4×4=16
16-(-1)=16+1=17
Answer: no it equal 17.
Step-by-step explanation: do 4 times 4 then you have 16-(-1) then change to 16+1 which equals 17.
helppppppppppppppp
Ginny and Bob are both locksmiths.
Ginny uses the function f(x)=60x+80 to determine the charge to her customers, where x represents the number of hours of labor.
The table shows what Bob charges a customer for x hours of labor.
x (hours) 0 1 2 3 4
cost ($) 60 140 220 300 380
Which locksmith charges less for an initial fee for a service call?
Drag a value or name to the boxes to correctly complete the statements.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Ginny charges Response area for an initial fee, and Bob charges Response area for an initial fee. Response area charges less for an initial fee.
For the initial fee, Bob charges less than Ginny.
What is unit rate?A unit rate means a rate for one of something.
Given that Ginny charges by uses the function f(x)=60x+80 where x represents the number of hours of labour.
Ginny initial charge = $80
Bob initial charge =$60
Hence, For the initial fee, Bob charges less than Ginny.
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What is the answer to this?
Answer:
2x+1=9
Step-by-step explanation:
\(\sqrt{2x+1}+5=2\)
\(\sqrt{2x+1}=-3\)
\(2x+1=9\)
If they want you to solve, then you can go farther.
2x=8
x=4
Check for extraneous solutions:
\(\sqrt{2(4)+1} +5 = 2\)
1. The slant height of a cone is 5cm and the radius of its base is 3cm. Find correct to the nearest
whole number the volume of the cone (A) 48cm3 (B) 47cm3 (C) 38cm3 (D)13cm3
The volume of the cone is 13 cm³. option D
How to determine the volumeTo determine the volume of the cone, we have that;
The formula for calculating the volume of a cone is expressed as;
Volume = (1/3)πr ²√(L ² - r ²).
Such that;
r is the radiusL is the slant heightSubstitute the values, we have;
Volume = 1/3 × 3.14 ² × √(25 - 9)
Find the squares, we get;
Volume, V = 1/3 × 9. 86 × √16
Find the square root
Volume, V = 1/3 × 9.86 × 4
Volume, V = 13 cm³
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what numbers add up to 6 but multiply to 77
Answer:
one
Step-by-step explanation:
one is the only number that evenly adds up to six and multplys to 77
NO LINKS!! Each graph represents a relation. Determine the domain and range. 2ii
Answer:
7) Domain: (-∞, ∞)
Range: [-1, ∞)
8) Domain: (-∞, ∞)
Range: (-∞, ∞)
Step-by-step explanation:
Interval notation
( or ) : Use parentheses to indicate that the endpoint is excluded.
[ or ] : Use square brackets to indicate that the endpoint is included.
Domain & Range
The domain is the set of all possible input values (x-values).
The range is the set of all possible output values (y-values).
Question 5From inspection of the graph, the line is continuous.
The arrows either end of the line indicate that the line continues indefinitely in those directions.
Therefore, the domain of the relation is unrestricted: (-∞, ∞)
From inspection of the graph, the minimum y-value is y = -1.
The end behavior of the relation is:
\(y \rightarrow + \infty, \textsf{as } x \rightarrow - \infty\)
\(y \rightarrow + \infty, \textsf{as } x \rightarrow +\infty\)
Therefore, the range of the relation is restricted: [-1, ∞)
Question 6From inspection of the graph, the line is continuous.
The arrows either end of the line indicate that the line continues indefinitely in those directions.
Therefore, the domain of the relation is unrestricted: (-∞, ∞)
The end behavior of the function is:
\(y \rightarrow + \infty, \textsf{as } x \rightarrow - \infty\)
\(y \rightarrow -\infty, \textsf{as } x \rightarrow +\infty\)
Therefore, the domain of the relation is unrestricted: (-∞, ∞)
Use the standard algorithm to find the product of 125 x 16.
Ok
Answer:
2,000
Step-by-step explanation:
125 x 16 = 2000
find the measure of
Answer:
angle RFG is 56
Step-by-step explanation:
Use the histogram to answer the following questions.
Frequency
The frequency of the class 90-93 is
The frequency of the class 94-97 is
This means that a total of
5.5
5
4.5
Your answers should be exact numerical values.
The frequency of the class 86-89 is
86
94
90
Duration of Dormancy (minutes)
dormancy periods were recorded.
The parameters that are needed to calculate a probability are listed as follows:
Number of desired outcomes in the context of a problem or experiment.Number of total outcomes in the context of a problem or experiment.Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.
The total number of periods is given as follows:
5 + 6 + 4 = 15.
The frequency of each class is given as follows:
86 - 89: 5/15 = 1/3.90 - 93: 6/15 = 2/5.94 - 97: 4/15.Learn more about the concept of probability at https://brainly.com/question/24756209
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Please, help me find the answer
The probability values for the questions posed are :
11/20probability of Public speaking given that student is majoring in Business Administration1/3A.)
Number of students Taking a public speaking class majoring in business administration.
10 + 45 = 55P(PS or BA) = 55/100 = 11/20
Therefore, the probability of PS or BA is 11/20
B.)
For the survey described, P(taken a public speaking class | majoring in Business Administration) represents the probability that a selected student has taken a public speaking class given that the student is majoring in business administration.
Hence, as inferred from P(A|B) ; probability of A given B.
C.)
P(PS|BA) = n(PSnBA) / n(BA)
n(PS) = 10+20 = 30
n(PSnBA) = 10
P(PS|BA) = 10/30 = 1/3
Therefore , the probability of PS|BA is 1/3.
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Need help with 10, 11, and 12. Need help fast!!
#10. In order to find a ratio, all we need to do is set up a simple equation and then cross-multiply!
I'll show you !
In this case, we'll take the already established ration (14 : 8 ) and find the equivalent ratio where 7 is in place of 14 (7: x)
x will be the other table value we are looking for!
Now let's set up the equation and cross-multiply!
\(\frac{14}{8} = \frac{7}{x}\)
cross multiply 14 and x, then 8 and 7
We get: 14x = 56
solve to find x!
x = 56/14
x = 4 blankets
Now let's use the ratio 7: 4 to find what goes with 16 in the table!
\(\frac{7}{4} = \frac{x}{16}\)
4x = 112
x = 112/4
x = 28 towels
_________________________________________________-
#11. : Using the same method, I'll fill in the values of the table on #11
16 forks, 10 spoons
8 forks, 5 spoons,
48 forks, 30 spoons
_____________________________________________
#12. If the neighbor pays you $17 for every 2 hours of work, we need to find how many times 2 hours goes in 8 hours of work
We do this by dividing
8/2 = 4 times
2 hours of work goes into 8, 4 times!
Now we multiply 4 by $17 to find how much your neighbor owes you!
$17 × 4 = $68
Your neighbor owes you $68 !!!
work out the area of this circle take pi to be 3.142 and write down all the digits given by your calculator diameter 13cm
Area of circle of diameter with 13cm is 132.74
What is area of circle?
The space a circle takes up in a two-dimensional plane is known as the area of the circle.Alternately, the area of the circle is the area included inside the circumference or perimeter of the circle. A = r², where r is the circle's radius, is the formula for calculating a circle's surface area. The square unit—for instance, m², cm², in², etc.—is the unit of area. In square units, the area of a circle is equal to r² or d²/4 where (Pi) = 22/7 or 3.14. The ratio of a circle's circumference to its diameter is known as pi (). This unique mathematical constant exists.Given :
Diameter of circle, d = 13cm
Radius of a circle, r = d/2
=13/2
=6.5
Area of circle = πr²
= 3.142 * 6.5 * 6.5
= 132.74
Hence, the Area of circle of diameter with 13cm is 132.74.
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Ms. Boyd has 9 bills in her purse that consist
of five-dollar bills and twenty-dollar bills. The
value of the bills is worth $105. How many
five-dollars bills and twenty-dollar bills does
Ms. Boyd have?
Answer:
5 twenty's 1 five
Step-by-step explanation:
20 x 5 = 100
100 = 5 = 105
How do you use positive and negative numbers in your everyday life?
These are just a few examples of how positive and negative numbers are used in everyday life. Understanding and using them correctly is essential for various fields, including mathematics, finance, science, and navigation.
Positive and negative numbers are commonly used in everyday life for a variety of purposes. Here are some examples:
Temperature: Positive and negative numbers are used to represent temperature. Positive numbers indicate higher temperatures, while negative numbers represent lower temperatures. For instance, if the temperature is 10 degrees Celsius, it is represented as +10°C, and if the temperature is -5 degrees Celsius, it is represented as -5°C.
Financial Transactions: Positive and negative numbers are used in financial transactions. Positive numbers represent income, gains, or credits, while negative numbers represent expenses, losses, or debits. When managing bank accounts or budgeting, positive and negative numbers are used to track inflows and outflows of money.
Direction and Coordinates: Positive and negative numbers are used to indicate direction and coordinates. In navigation, positive and negative numbers are used to represent east and west directions or north and south coordinates. For example, a latitude of +40 degrees represents a location north of the equator, while a longitude of -75 degrees represents a location west of the prime meridian.
Sports Scores: Positive and negative numbers are used to keep track of scores in sports. In games such as basketball, soccer, or football, positive numbers represent points scored by a team, while negative numbers represent points scored against the team.
Elevations: Positive and negative numbers are used to represent elevations or heights above or below sea level. Positive numbers indicate locations above sea level, while negative numbers represent locations below sea level. This is particularly relevant in geography, construction, and aviation.
Debt and Credit: Positive and negative numbers are used to represent debt and credit. Positive numbers indicate money owed or credit received, while negative numbers represent payments made or credit used. It is commonly used in accounting, loans, credit cards, and personal finance.
These are just a few examples of how positive and negative numbers are used in everyday life. Understanding and using them correctly is essential for various fields, including mathematics, finance, science, and navigation.
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what type of information is used to obtain information on how scores are spread from the center of a distribution
Answer:
You need variability
Step-by-step explanation:
Variability measures the degree to which the scores are spread out or clustered together in a distribution.
Hope this helps:)
Pete’s Painting charges $25 per room to paint, plus an additional $0.50 per square foot that they paint. If they charged me $201 to paint my kitchen, how many square feet did they paint?
Answer:
352 square feet
Step-by-step explanation:
201-25=176
176/.50=352 square feet
The sum of two numbers is 48 and the difference is 22 what are the numbers
Answer:
35 and 13
Step-by-step explanation:
Sum: 35 + 13 = 48
Difference: 35 - 13 = 22
five times the sum of the digits of a two digit number is 9 less than the number formed by reversing its digits . if four times the value of the digit at ones place is equal to half of the place value of the digit at tens place, find the numbers
9514 1404 393
Answer:
45
Step-by-step explanation:
Let x and y represent the tens and ones digits, respectively. The 5 times the sum of digits is 5(x+y). The value of the digit-reversed number is (10y+x), so the required relation is ...
5(x +y) = (10y +x) -9
The other relationship between the digits is given as ...
4y = 1/2(10x)
A graphing calculator shows the solution to these equations is (x, y) = (4, 5).
The two-digit number is 45.
__
Additional comment
You can solve these equations in any of a variety of ways. Using a graphing calculator to find integer solutions is fast and easy, so is one of my favorites. Here, the coefficients on one equation are not easy multiples of those in the other, so substitution and/or elimination can get messy. In this situation, I like to use the "cross-multiplication" method, which starts with the equations in general form:
4x -5y +9 = 05x -4y +0 = 0From the coefficients of these equations, differences of cross products are formed:
d1 = 4(-4) -(5)(-5) = 9d2 = -5(0) -(-4)(9) = 36d3 = 9(5) -0(4) = 45Then the solutions are the solutions to 1/d1 = x/d2 = y/d3:
x = d2/d1 = 36/9 = 4y= d3/d1 = 45/9 = 5(x, y) = (4, 5) ⇒ the number is 45.
__
This method is one of several variations of Cramer's Rule, the general solution of systems of linear equations using matrix methods.
if f(x)=x+2/x^2-9 and g(x)=11/x^2+3x
A. find f(x)+g(x)
B. list all of the excluded values
C. classify each type of discontinuty
To receive credit, this must be done by Algebraic methods, not graphing
The types of discontinuities are: removable discontinuity at x = -3 and vertical asymptotes at x = 0 and x = 3.
A. To find f(x) + g(x), we add the two functions together:
f(x) + g(x) = (x + 2)/(x^2 - 9) + 11/(x^2 + 3x)
To add these fractions, we need a common denominator. The common denominator in this case is (x^2 - 9)(x^2 + 3x). So, we rewrite the fractions with the common denominator:
f(x) + g(x) = [(x + 2)(x^2 + 3x) + 11(x^2 - 9)] / [(x^2 - 9)(x^2 + 3x)]
Simplifying the numerator:
f(x) + g(x) = (x^3 + 3x^2 + 2x^2 + 6x + 11x^2 - 99) / [(x^2 - 9)(x^2 + 3x)]
Combining like terms:
f(x) + g(x) = (x^3 + 16x^2 + 6x - 99) / [(x^2 - 9)(x^2 + 3x)]
B. To find the excluded values, we look for values of x that would make the denominators zero, as division by zero is undefined. In this case, the excluded values occur when:
(x^2 - 9) = 0 --> x = -3, 3
(x^2 + 3x) = 0 --> x = 0, -3
So, the excluded values are x = -3, 0, and 3.
C. To classify each type of discontinuity, we examine the excluded values and the behavior of the function around these points.
At x = -3, we have a removable discontinuity or hole since the denominator approaches zero but the numerator doesn't. The function can be simplified and defined at this point.
At x = 0 and x = 3, we have vertical asymptotes. The function approaches positive or negative infinity as x approaches these points, indicating a vertical asymptote.
Therefore, the types of discontinuities are: removable discontinuity at x = -3 and vertical asymptotes at x = 0 and x = 3.
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Certain advertisers would like to estimate the proportion of viewers who spend the majority of their television time
watching alone. The consensus is that this percentage has been increasing over the years due to the increased
number of television sets in households.
a. Determine the sample size needed to construct a 90% confidence interval with a margin of error of no more than
6% to estimate the true proportion of viewers who watch television alone.
b. What impact would a pilot sample that showed that 44% of viewers spend the majority of their television time
watching alone have on your on results.
a. The sample size needed is
(Round up to the nearest integer.)
b. The new sample size needed would be 0
(Round up to the nearest integer.)
Answer:
Step-by-step explanation:
find the theoretical probability.
\(|\Omega|=8\\|\text{odd}|=4\\\\P(\text{odd})=\dfrac{4}{8}=\dfrac{1}{2}\)
Answer:
4/8
or, 1/2
Step-by-step explanation:
odd numbers (O) = (1,3,5,7) = 4
total numbers (T) = 8
P(odd) = n(O)/n(T)
= 4/8
Order cube root of eighty-eight, twenty-eight ninths, square root of nineteen from greatest to least.
cube root of eighty-eight, twenty-eight ninths, square root of nineteen
twenty-eight ninths, square root of nineteen, cube root of eighty-eight
twenty-eight ninths, cube root of eighty-eight, square root of nineteen
cube root of eighty-eight, square root of nineteen, twenty-eight ninths
Answer:
(a) twenty-eight ninths, square root of nineteen, cube root of eighty-eight
Step-by-step explanation:
When ordering a list of numbers by hand, it is convenient to convert them to the same form. Decimal equivalents are easily found using a calculator.
OrderThe attachment shows the ordering, least to greatest, to be ...
\(\dfrac{28}{9}.\ \sqrt{19},\ \sqrt[3]{88}\)
__
Additional comment
We know that √19 > √16 = 4, and ∛88 > ∛64 = 4, so the fraction 28/9 will be the smallest. That leaves us to compare √19 and ∛88, both of which are near the same value between 4 and 5.
One way to do the comparison is to convert these to values that need to have the same root:
√19 = 19^(1/2) = 19^(3/6) = sixthroot(19³)
∛88 = 88^(1/3) = 88^(2/6) = sixthroot(88²)
The roots will have the same ordering as 19³ and 88².
Of course, these values can be found easily using a calculator, as can the original roots. By hand, we might compute them as ...
19³ = (20 -1)³ = 20³ -3(20²) +3(20) -1 = 8000 -1200 +60 -1 = 6859
88² = (90 -2)² = 90² -2(2)(90) +2² = 8100 -360 +4 = 7744
Then the ordering is ...
28/9 < 19³ < 88² ⇒ 28/9 < √19 < ∛88
Answer:
the ordering is
28/9 < 19³ < 88² ⇒ 28/9 < √19 < ∛88
Step-by-step explanation:
PLZ HELPPP
6.7 multiplied by 8
Answer:
53.6
Step-by-step explanation:
Answer:
53.6 is the answer :D
Step-by-step explanation:
The table below shows the lengths and weights of six dolphins at an aquarium. Use the data from Pax and Snowflake to create a linear model that predicts the weight (y) of a dolphin given its length (x). Which dolphin's weight differs most from the value predicted by this model?
The dolphin's weight that differs most from the value predicted by this model is JoJo's (31 lb of difference)
Let's elaborate the model this way:
Snowflake's length - Pax's length = 8.2 - 7.6 = 0.6 ft
Snowflake's weight - Pax's weight = 549 - 519 = 30 lb
Ratio = 30/0.6 = 50 lb/ft
This means that for every foot of length, the dolphin has a variable weight of 50 lb.
However, if we multiply the ratio by the actual length of the two dolphins, we will have these results:
Snowflake = 50 × 8.2 = 410
Pax = 50× 7.6 = 380
Snowflake = Actual weight - Ratio× Length = 549 - 410 = 139
Pax = Actual weight - Ratio × Length = 519 - 380 = 139
The common difference is 139.
Therefore, the linear model that predicts the weight (y) of a dolphin given its length (X) is:
y = 139 + 50x
Now, let's use the linear equation or model to calculate the weight of the remaining four dolphins, as follows:
Blaze y = 139 + 50 × 6.8 = 479 ⇒ difference of 9 lb (488 - 479)
JoJo y = 139 + 50 × 5.8 = 429 ⇒ difference of 31 lb (460 - 429)
Corky y = 139 + 50 ×8.4 = 559 ⇒ difference of 2 lb (559 - 557)
Shadow y = 139 + 50 × 7.4 = 509 ⇒ difference of 8 lb (509 - 501)
Hence, the dolphin's weight that differs most from the value predicted by this model is JoJo's (31 lb of difference)
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The table below shows the lengths and weights of six dolphins at an aquarium. Use the data from Pax and Snowflake to
create a linear model that predicts the weight (y) of a dolphin given its length (X). Which dolphin's weight differs most from th
value predicted by this model?
Name
Snowflake
Shadow
Corky
Pax
JoJo
Blaze
Length (ft)
8.2
74
8.4
7.6
5.8
6.8
Weight (lb)
549
501
557
519
460
488
Blaze
JOJO
Corky
Shadow
what are the zeros of f(x)=2x^3+5x^2-2x-5, if one of the zeros is 1?
Answer:
x = -5/2, -1, 1
Step-by-step explanation:
Step 1: Factor
2x³ + 5x² - 2x - 5(2x + 5)x² - 2x - 5 (2x + 5)(x - 1)(x + 1)Step 2: Replace y with 0
"f(x)" is the same as "y = "
0 = (2x + 5)(x - 1)(x + 1)Case 1: (5 + 2x) = 05 + 2x = 02x = -5x = -5/2Case 2: (x - 1) = 0x - 1 = 0x = 1Case 3: (x + 1) = 0x + 1 = 0x = -1-Chetan K
a. Bared an the information in the figure, which of the two cities have nearest to each other?
Select choice
b. Based on the information in the figure, which of the two cities are farthest apart from each other?
Select Choice
c. If you were going to use the information from 5 Sate's sketch to plan a road trip between these cities, what is an assumption that you would have to make?
Select Choice
The City A and Abilene are nearest to each other
The Austin and Abilene are farthest apart from each other
Here the two angles of the triangle = 59 degrees and 64 degrees
The sum of the angles in a triangle is 180 degrees
Then the third angle will be
59 + 64 + x = 180
123 + x = 180
x = 180 - 123
x = 57 degrees
The third city name is not visible so consider it as city A
Part a
Here the smallest angle is 57 degrees
Opposite side of the angle will be the smallest distance
That is the distance between city A and Abilene
Part b
Here the largest angle is 64 degrees
The opposite side of the angle will be largest distance
That is the distance between Austin and Abilene
Therefore, the City A and Abilene are nearest to each other and Austin and Abilene are farthest apart from each other
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2. A bicycling club has 58 members, of which 4 are males and the rest are females. What is the ratio of females to males?
please help is ratio
Answer: 54:4
Step-by-step explanation:
y=9/4×2
sketch the graph of f and f on the same set of axes
The graph of the function \(f(x) = (9/4)x^2\) is a symmetric upward-opening parabola.
The graph represents a parabola that opens upward. As x increases, the corresponding y-values increase, forming a curved shape. The vertex of the parabola is at the origin (0,0). The graph is symmetric with respect to the y-axis, meaning that the left and right sides of the parabola are mirror images of each other.The slope of the graph gradually increases as x moves away from the origin. The steepness of the curve becomes more pronounced, indicating a faster rate of increase in y-values for larger x-values.The graph does not intersect the x-axis, indicating that there are no real roots or solutions for the equation f(x) = 0. The y-intercept of the graph is at (0, 0), and the y-values increase indefinitely as x approaches positive or negative infinity.Overall, the graph represents a quadratic function with a positive leading coefficient, resulting in an upward-opening parabolic curve. The graph has been attached.
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What property is 4(2+c)+5