The approximate length of side XY is
units
The approximate length of side YZ
units.
The approximate length of side ZX is
v units.
The approximate perimeter of triangle XYZ is
units
Answers
please mark me brainlieset and click the stars i spent so long on this :>
Answer:
ZX = 3√2, XY =√10, YZ = 4, Perimeter of ΔXYZ = 14√5 units
Step-by-step explanation:
1. We can see that if we were to draw an altitude from vertex X to side ZY of this triangle, the length of this altitude would be: 3 units
2. The length of ZX can be determined through Pythagorean Theorem. If this altitude were to be called XW, it would be one of the legs of a mini triangle ZXW, along with leg ZW. ZW clearly = 3, thus ZX^2 = 3^2 + 3^2 = 18, and ZX = √18 units = 3√2.
3. The same thing can be applied to another "mini" triangle YXW. This triangle would have legs XW (altitude of the triangle ZXY) and YW. Knowing XW to have a length of 3 units, and YW to have length of 1 unit ⇒ XY^2 = XW^2 + YW^2 = 3^2 + 1^2, and XY = √10.
4. YZ is visualized to have a length of 4 units.
5. Knowing that ZX = 3√2, XY =√10, and YZ = 4 ⇒ Perimeter of ΔXYZ = ZX + XY + YZ = 3√2 + √10 + 4 = 14√5 units. To simplify this, it would be that the Perimeter of ΔXYZ = 14√5 units
ZX = 3√2, XY =√10, YZ = 4, Perimeter of ΔXYZ = 14√5 units
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
1. We can see that if we were to draw an altitude from vertex X to side ZY of this triangle,
the length of this altitude would be: 3 units
2. The length of ZX can be determined through Pythagorean Theorem.
If this altitude were to be called XW, it would be one of the legs of a mini triangle ZXW, along with leg ZW.
ZW clearly = 3,
thus
[tex]ZX^2 = 3^2 + 3^2 = 18[/tex],
and ZX = √18 units = 3√2.
3. The same thing can be applied to another "mini" triangle YXW. This triangle would have legs XW (altitude of the triangle ZXY) and YW.
Knowing XW to have a length of 3 units, and YW to have a length of 1 unit [tex]= > XY^2 = XW^2 + YW^2 \\= > 3^2 + 1^2[/tex],
and XY = √10.
4. YZ is visualized to have a length of 4 units.
5. Knowing that
ZX = 3√2, XY =√10, and YZ = 4
⇒ Perimeter of ΔXYZ = ZX + XY + YZ
⇒ Perimeter of ΔXYZ = 3√2 + √10 + 4
⇒ Perimeter of ΔXYZ = 14√5 units.
To simplify this, it would be that the Perimeter of ΔXYZ = 14√5 units
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Related Questions
6
4
2
Divide (16x - 12x + 4x) by 4x
Answers
Answer:2
Step-by-step explanation:
Combine like terms and divide
8x/4x
2
3. Identify the graph described by the function
P(x)= x/10 for x = 1, 2, 3, and 4.
Answers
Answer:
D
Step-by-step explanation:
if x = 1
P(x) = 1/10
if x = 2
P(x) = 2/10
if x = 3
P(x) = 3/10
if x = 4
P(x) = 4/10
Solve the following absolute value equation.
4|x + 6 = 24
x = [?]
= -0
X =
Enter
Answers
x = 12, using the concept of absolute value equation.
What is absolute value equation?The non-negative value of a real number x, regardless of its sign, is its absolute value (or modulus), | x |. For instance, 5 has an absolute value of 5, and 5 has a value of 5. One way to think about a number's absolute value is as its distance from zero on the real number line.
To answer an absolute value problem, isolate the absolute value on one side of the equation. Then, resolve both equations by setting their respective contents to the positive and negative values of the integer on the other side of the equation.
Given that,
4|x+6| = 24
either |x+6| = 6 or, |x+6| = -6
x = 0. -12
So, x = 12 [here as negative sign is already present]
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Based on the given information determine which sides of quadrilateral ABCD must be parallel
Answers
Answer: AB || DC (1st choice)
Reason:
Angles A and D add to A+D = 59+121 = 180Angles B and C add to B+C = 37+143 = 180We have two pairs of consecutive interior angles that are supplementary. We then use the converse of the consecutive interior angles theorem to conclude side AB is parallel to DC. This means ABCD is a trapezoid.
Refer to the diagram below.
help meeeeeeeeeee pleaseee
Answers
a. The population of the state in 2000 is 18.5 million
b. The population will reach 26.6 million in about 2 years
Determining population using a formulaFrom the question, we are to determine the population of the state in 2000.
From the given information,
The formula that models the population of the US state after 2000 is
A = 18.5e^(0.1708t)
To determine the population of the state in 2000, we will substitute t = 0
That is,
A = 18.5e^(0.1708(0))
A = 18.5e^(0)
A = 18.5(1)
A = 18.5
Thus, the population of the state in 2000 is 18.5 million
b. To determine when the population will reach 26.6 million
Substitute A = 26.6 in the equation
A = 18.5e^(0.1708t)
26.6 = 18.5e^(0.1708t)
Solve for t
26.6/18.5 = e^(0.1708t)
ln(26.6/18.5) = 0.1708t
0.36314048 = 0.1708t
t = 0.36314048/0.1708
t = 2.126
t ≈ 2
Hence, the population will reach 26.6 million in about 2 years
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How to do this question?
Answers
The solution set for absolute value inequalities are presented as follows;
(b) (i) -∞ < x ≤ 2
(ii) 1.25 ≤ x < 3, or x > 3
What is an absolute value inequality?An absolute value inequality is an inequality with an absolute value expression containing a variable.
(i) |2·x + 7| + 1 ≥ 6·x
Solving for when |2·x + 7| is positive, we get;
2·x + 7 + 1 ≥ 6·x
7 + 1 ≥ 6·x - 2·x = 4·x
8 ≥ 4·x
Dividing both sides by 4, we get;
8 ÷ 4 ≥ 4·x ÷ 4 = x
2 ≥ x
Therefore; x ≤ 2
The solution of the absolute value inequality can be found as follows;
|2·x + 7| + 1 ≥ 6·x
|2·x + 7| ≥ 6·x - 1
Therefore, we have the following compound inequality;
2·x + 7 ≤ -(6·x - 1), 2·x + 7 ≥ (6·x - 1)
The solution for the inequality, 2·x + 7 ≤ -(6·x - 1) is found as follows;
2·x + 7 ≤ -(6·x - 1) = 1 - 6·x
2·x + 6·x ≤ 1 - 7 = 6
8·x ≤ 6
x ≤ 6/8 = 3/4
x ≤ 3/4
The solution for the inequality, 2·x + 7 ≥ (6·x - 1) is found as follows;
2·x + 7 ≥ (6·x - 1)
7 + 1 ≥ 6·x - 2·x = 4·x
8 ≥ 4·x
x ≤ 2
Combining the solution, we get;
-∞ < x ≤ 2
(ii) [tex]\left|\dfrac{2\cdot x+ 1}{x - 3} \right| \geq 2[/tex]
Therefore, we get;
[tex]\dfrac{2\cdot x+ 1}{x - 3} \leq -2[/tex]
[tex]\dfrac{2\cdot x+ 1}{x - 3} + 2 \leq 0[/tex]
[tex]\dfrac{4\cdot x - 5}{x - 3} \leq 0[/tex]
x < 3, or x ≥ 1.25
1.25 ≤ x < 3
[tex]\dfrac{2\cdot x+ 1}{x - 3} \geq 2[/tex]
[tex]\dfrac{2\cdot x+ 1}{x - 3} -2 \geq 0[/tex]
[tex]\dfrac{7}{x - 3} \geq 0[/tex]
Therefore, x > 3,
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Here are four equations of absolute value functions and three coordinate pairs. Each coordinate pair represents the vertex of the graph of an absolute value function.
A. p(x)=[x-9] B. q(x)=[x]+9 C. r(x)=[x+9] D. t(x)=[x]-9
Answers
The vertex of p(x) is (9, 0).
Vertex of q(x) is (0, 9).
Vertex of r(x) is (-9, 0).
Vertex of t(x) is (0, -9).
What is absolute value function?
The non-negative value of a real number x without regard to its sign is known as its absolute value or modulus in mathematics and is denoted by the symbol |x|. Specifically, |x|=x and |x|=-x, respectively, if x is a positive number, and |0|=0 otherwise.
The vertex form of an absolute value function is f(x) = a |x - h| + k where
(h, k) is the vertex from which the graph starts and a = m is the slope.
So, the absolute value function p(x) = |x - 9|, means h =-(-9) = 9 and
k = 0, will result in the vertex at (9, 0).
The absolute value function q(x) = |x| +9 , means h = 0 h=0 and k =9, will result in a vertex (0, 9).
The absolute value function r(x) = |x + 9|, means, h = -9 and, k=0, will result in the vertex at (-9, 0).
The absolute value function t(x) = |x| -9 , means h = 0 and k = -9, will result in the vertex at (0, -9)
Hence,
The vertex of p(x) is (9, 0).
Vertex of q(x) is (0, 9).
Vertex of r(x) is (-9, 0).
Vertex of t(x) is (0, -9).
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CAN SOMEONE HELP WITH THIS QUESTION?✨
Answers
The function that describes the exponential growth is P(t) = 21100 [tex]e^{0.09t}[/tex] and the population in 2008/ will be 43348.54.
What is an exponential function?In mathematics, an exponential function is a relationship of the type y = ax, where x is an independent variable that spans the entire real number line and is expressed as the exponent of a positive number.
(a)
As per the given,
Growth rate r = 9 % = 0.09
Population in 2000 (t = 0) is 21100
The formula for exponential growth is given as,
P(t) = P₀e^(rt)
P(t) = 21100 e^(0.09 x t)
P(t) = 21100 [tex]e^{0.09t}[/tex]
(b)
The number of population in 2008 (t = 8) will be as.,
P(8) = 21100 e^(0.09 x 8)
P(8) = 43348.54
Hence "The function that describes the exponential growth is P(t) = 21100 [tex]e^{0.09t}[/tex] and the population in 2008/ will be 43348.54".
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help meeeeeeeeeee pleaseee
Answers
18.5 is correct for part (a) since t = 0 leads to A = 18.5
=====================================================
Part (b)
Your teacher is asking for the value of t when A = 26.6
A = 18.5*e^(0.1708t)
26.6 = 18.5*e^(0.1708t)
26.6/18.5 = e^(0.1708t)
1.437838 = e^(0.1708t)
Ln(1.437838) = 0.1708t
t = Ln(1.437838)/0.1708
t = 2.126116 approximately
t = 2 when rounding down to the nearest integer
Therefore, 2 years after the year 2000, the year 2002, is when the population reaches roughly 26.6 million. The actual population will be slightly less than 26.6 million, but it's close enough.
Note that:
18.5*e^(0.1708*2) = 26.033 approximately18.5*e^(0.1708*3) = 30.882 approximatelywhich helps confirm the correct value of t is between t = 2 and t = 3.
Answer: 2002The assets and liabilities of a lawyer are listed below.
Car Value
Car Loan
Savings Account Balance
Season Baseball Tickets
$41,450
$22,890
$13,547
$19,400
Student Loans
$12,410
Credit Card Balance
$19,420
Checking Account Balance $16,309
Home Value
$271,345
What is the lawyer's net worth?
O $307,331
O $312,795
O $342,651
O $362,051
Answers
The lawyer's net worth is $307,331.
What are Assets and Liabilities?Assets are those things the organization or the individual possess. It is a source of income.
Liabilities are those items that are debt or has to pay money for it.
From the list, the assets of the lawyer are:
Car value = $41,450
Savings account balance = $13,547
Season baseball tickets = $19,400
Checking account balance = $16,309
Home Value = $271,345
Total assets = $41,450 + $13,547 + $19,400 + $16,309 + $271,345
= $362,051
The liabilities of the lawyer are:
Car loan = $22,890
Student loans = $12,410
Credit card balance = $19,420
Total liabilities = $22,890 + $12,410 + $19,420
= $54,720
Net worth = Total assets - Total liabilities
= $362,051 - $54,720
= $307,331
Hence, the net worth of the lawyer with these assets and liabilities is $307,331.
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5 Make a Plan How will you solve? Explain.
3. An athlete ran a total of 1,500 kilometers in races before retiring. The athlete finished thirty-two 15-kilometer races. The rest were 10-kilometer races. How many of the races were 10-kilometer races?
Answers
The number of races that were 10-kilometer long is 102.
An athlete ran a total of 1,500 kilometers in a race before retiring. The athlete completed 32 races that were at least 15 kilometers in length. The rest were 10-kilometer races. We need to find out the number of races that were 10-kilometer long.
Let the number of races that were 10-kilometers long be denoted by the variable "x". An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equal sign. We can write the equation as given below.
32×15 + 10x = 1,500
480 + 10x = 1,500
10x = 1,500 - 480
10x = 1,020
x = 1,020/10
x = 102
Hence, the number of races that were 10-kilometer long is 102.
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Write the quadratic equation whose roots are 6 and -4, and whose leading coefficient is 1.
(Use the letter x to represent the variable.)
Answers
The quadratic equation is x² - 2x - 24
What is quadratic equation ?
Any equation in algebra that can be written in standard form as where x stands for an unknown value and a, b, and c stand for known values is said to be a quadratic equation. In general, it is assumed that a > 0; equations with a = 0 are regarded as degenerate since they become linear or even simpler.
Square and quadrangle difficulties have a close relationship with quadratic equations (another name for rectangles). In actuality, the Latin word quadratus, which means square, is the root of the word quadratic.
Any quadratic problem can be solved using the quadratic formula. The equation is first changed to have the form ax2+bx+c=0, where a, b, and c are coefficients. After that, we enter these coefficients into the following formula: (-b(b2-4ac))/(2a).
Given roots of quadratic equation are 6 and -4.
Also given here leading coefficient is 1.
We know that, the formulae for forming quadratic equation when its roots are given is as follows: x² - (α+β)x + αβ
Here α and β are the roots of the quadratic equation.
Let α = 6 and β = -4
Putting the value of in the above formulae we get,
x² - (6-4)x - 24
x² - 2x - 24
But remember here 1 is the leading coefficient of the quadratic equation with roots 6 and -4 (given in question),so we have to multiply the equation by 1 to get the final answer.
So, Hence the required quadratic equation is x² - 2x - 24
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Home Depot sells boards in 3 meter lengths. How much board is left if you only need 1 meter and 45 cm?
Answers
If you only need 1 meter and 45 cm. Then the length of the board left will be 1.55 meters.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
Conversion means converting the same thing into different units.
Home Depot sells boards in 3-meter lengths. If you only need 1 meter and 45 cm. Then the length that you need is calculated as,
⇒ 1 meter and 45 centimeters
Convert the centimeters into a meter. Then we have
⇒ 1 + 45 / 100
⇒ 1 + 0.45
⇒ 1.45
Then the length of the board left will be calculated as,
⇒ 3 - 1.45
⇒ 1.55 meters
If you only need 1 meter and 45 cm. Then the length of the board left will be 1.55 meters.
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Y=k√x and y=7 and x=9. What is the value of y when x=36
Answers
Answer:
y = 14
Step-by-step explanation:
y = k[tex]\sqrt{x}[/tex] Solve for k
7 = k[tex]\sqrt{9}[/tex]
7 = k3 Divide both sides by 3 to solve for k
[tex]\frac{7}{3}[/tex] = k
y = kx
y = [tex]\sqr\frac{7}{3} }[/tex][tex]\sqrt{36}[/tex]
y = [tex]\frac{7}{3}[/tex](6)
y = 14
[tex]\frac{7}{3}[/tex][tex](\frac{6}{1})[/tex] is the same thing as [tex]\frac{7}{1}[/tex][tex](\frac{2}{1})[/tex] I cross canceled the 3 and the 6
[tex]\frac{14}{1}[/tex] = 14
A test is worth 100 points. Each problem is worth either 2 points or 5 points. The number of 5-point problems is 22 fewer than the number of 2-point problems. How many problems of each type are on the test?
There are___five point problems
There are___two point problems
Answers
Answer: 8 Five point questions
Step-by-step explanation:
Hope this helps you!
Use the Quadratic Formula to solve the equation
Answers
Answer:
Step-by-step explanation:
Use the graphic organizer to answer the question.
Which action correctly completes this graphic organizer?
Ask a question
Seek input from others
Read scholarly sources
Make analogy comparison
Answers
Ask a question action correctly completes this graphic organizer.
Option A is correct .
What graphic organizer means?A graphic organizer is a visual and graphic display that depicts the relationships between facts, terms, and or ideas within a learning task.Graphic organizers are also sometimes referred to as knowledge maps, concept maps, story maps, cognitive organizers, advance organizers, or concept diagrams
.Ask a question action correctly completes this graphic organizer.
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Walt made an extra $7000 last year from a part-time job. He invested part of the money at 7% and the rest
at 8%. He made a total of $530 in interest. How much was invested at 8%?
Answers
The amount invested at the rate of 8% is; $3000
How to calculate the amount invested?We are told that Walt made an extra $7000 last year from a part-time job. He invested part of the money at 7% and the rest at 8%.
If the amount invested is denoted as X , then we have;
0.07X + 0.08(7000 - X)
Now, since he made a total of $530, the we can equate that equation to $530 to get;
0.07X + 0.08(7000 - X) = 530
Expanding this equation gives us;
0.07X + 560 - 0.08X = 530
0.01X = 560 - 530
0.01X = 30
X = 30/0.01
X = $3000
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Solve the given equation
2 x+3 y-6
x+y=6
Answers
Answer:
= 2x=6-3y
= 2x/2= 6-3y/2
= x= 6-3y/2
= x = -3y/2+3
PLEASE HELP ME WITH THIS QUESTION
Answers
a) Corresponding angles are congruent, m<a=139
b) Alternate Interior Angles are congruent, m<b =139
Solve the system of equations below by
graphing. Type in the ordered pair (x,y)
for your answer
y=-2
x+y=5
Answers
Answer:
(7, -2)
Step-by-step explanation:
You want a graphical solution to the equations ...
y = -2x + y = 5GraphThe graph is shown in the attachment. The solution is (x, y) = (7, -2).
Savannah buys a $40 gift card to her favorite smoothie shop. Each smoothie costs $4. She wants to have at least $10 left on her card at the end of this month. The inequality below relates x, the number of smoothies she could buy between now and the end of this month with her gift card balance.
40 minus 4 x greater-than-or-equal-to 10
Answers
The choice that best describes the number of smoothies that Savannah could buy between now and the end of this month with her gift card balance is "She can buy from 0 to 7 smoothies, but no more."
How to find the number of smoothies that Savanna can buy?
Given : 40 - 4x > 10 which is an inequality
To find : The value of x
Procedure:
Step 1: Collect all the terms with x on right side and the constant terms on the left side of the greater sign.
40 - 4x > 10
When 10 is brought to the left, there will be change in sign for the number 10 and similarly, when -4x is taken to the right, it becomes +4x or simply 4x. So inequality becomes
40 - 10 > 4x
Step 2: On solving the resulting inequality, we get
30 > 4x
Divide both sides by 4. So inequality becomes
[tex]\frac{30}{4} > \frac{4x}{4}[/tex]
7.5 > x
This means, x < 7.5
The choice that best describes the number of smoothies that Savannah could buy between now and the end of this month with her gift card balance is "She can buy from 0 to 7 smoothies, but no more."
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Answer:She can buy from 0 to 7 smoothies, but no more."
Step-by-step explanation:She can buy from 0 to 7 smoothies, but no more." Which is option B
Write down in terms of n, an expression for the nth term of the following sequences:
a) 12 10 8 6 4
b) 25 20 15 10 5
Answers
b) T(n) = 30 - 5n
help plase thanks you
Answers
The values to make up the solution set of inequality are {8,9,10}.
What is meant by inequality?In mathematics, an unjust comparison between two numbers or other mathematical expressions is referred to as an inequality.
A less than symbol (a, b) denotes that one thing is less than the other.
The notation a > b indicates that an is greater than b.
A and b are not equal in either situation. A strict inequality is one in which an is strictly less than or strictly bigger than b in certain connections. Comparability is left out.
First we have to replace m with 8, it becomes:
8+7 =15<18
For 9,
9+7 =16<18
For 10,
10+7 =17<18
And for 11,
11+7 =18=18
So, The values to make up the solution set of inequality are {8,9,10}.
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Find a polynomial P3 such that {po, P1, P2, P3} (see Ex- ercise 11) is an orthogonal basis for the subspace P3 of P4. Scale the polynomial p3 so that its vector of values is (-1,2,0, -2,1).
Answers
The equation of the polynomial P3 is p3(t) = 5/6t³− 17/6t
Equation:
In algebra, an equation consists of variable, number and constants.
Given,
Here we need to find the polynomial P3 such that {P0, P1, P2, P3} is an orthogonal basis for the subspace P3 of P4.
And the scale the polynomial p3 so that its vector of values is (-1,2,0, -2,1).
Here we know that the polynomial (before the scaling) p3 is just the difference between t³ and its orthogonal projection on the span of 1,t,t²−2.
Then we showed that the projection is , hence
p3(t) = t³− 17/5t
When here we have the scale this polynomial such that the vector of values at t=−2,−1,0,1,2 is (−1,2,0,−2,1).
Now, we need to find the scalar α, it can be written as,
=> α⋅p3(−2)=−1
=> α⋅p3(−1)=2
=> α⋅p3(0)=0
=> α⋅p3(1)=−2
=> α⋅p3(2)=1
Here from the 4-th equation we have the value of
=> α⋅(1- 17/5) = -2
=> α = 5/6
And it is easy to check that all the equations are satisfied with this α.
Therefore, the required polynomial p3 is
=> p3(t) = 5/6(t³− 17/5t)
=> p3(t) = 5/6t³− 17/6t
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A mathematics teacher wanted to see the correlation between test scores and homework. The homework grade x and test grade (y) are given in the accompanying table. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest hundredth. Using this equation, find the projected test grade, to the nearest integer, for a student with a homework grade of 39 .
Answers
The linear regression for the given data is y = 0.8x + 12.78 and the test grade will be 44.
What is linear regression?
A variable's value can be predicted using linear regression analysis based on the value of another variable. The dependent variable is the one you want to be able to forecast. The independent variable is the one you're using to make a prediction about the value of the other variable.
Based on the given data
Using the graphing calculator, the linear regression will be,
y = 0.8x + 12.78
For a homework grade of 39, x = 39
Then, y = 0.8*39 + 12.78 = 43.98 ≈ 44
Hence, the test grade will be 44.
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Answer:
Step-by-step explanation:
Please help, i cannot figure out how to solve for 60%
Answers
(a) As time goes on and approaches infinity, the level of oxygen in the pond approaches normal, therefore;
The oxygen level will eventually approach its normal level in the long-run
(b) The number of weeks after which the oxygen level becomes 60% of its normal level are 0.5, 2 weeks
How can the rational polynomial be evaluated?The rational polynomial function in which the numerator and denominator have the same power and the coefficient of the highest power are the same indicates that the value of f(t) approaches 1 (normal) as t approaches infinity.
The function with which the oxygen level in the pond can be found is presented as follows;
[tex]f(t) = \dfrac{t^2-t + 1}{t^2+ 1}[/tex]
f(0) = 1, therefore
The end behavior of the function as the value ot t approaches infinity is therefore the asymptote;
y = 1/1 = 1
The value of the function f(t) as the value of t approaches infinity is that the f(t) approaches 1, which is the normal level of oxygen in the pond
(b) When the oxygen level is 60%, we get;
[tex]f(t) = \dfrac{t^2-t + 1}{t^2+ 1} = 60\% = 0.6[/tex]
0.6·(t² + 1) = t² - t + 1
0.6·t² + 0.6 = t² - t + 1
0.4·t² - t + 0.4 = 0
t² - 2.5·t + 1 = 0
Therefore;
(t - 2)·(t - 0.5) = 0
t = 2 or t = 0.5
The times when the oxygen level is 60% is 0.5 and 2 weeks after the organic waste is dumped in the pond.
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Cesar invested a total of $41000 in two accounts. The first account earned 7% after one year. However the second account suffered a 5% loss in the same time. At the end of one year the total amount of money gained was $1670. How much he invested in each account?
Answers
He invested in each account as follows:
First account -----> 31,000
Second account -----> 10,000
What is the percentage?
It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
gained - lost = 1670
0.07x - 0.05(41000 - x) = 1670
Find x :
0.07x - 0.05(41000 - x) = 1670
0.07x - 2050 + 0.05x = 1670
0.12x = 1670 + 2050
x = 31,000
41000 - 31,000 = 10,000
He invested in each account as follows:
First account -----> 31,000
Second account -----> 10,000
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Tami rolled a die 20 times. 14 times it landed on an even number; 6 times it landed on an odd number. How does the experimental and theoretical probability compare, for rolling an odd number?
A)
The theoretical probability is higher.
B)
The experimental probability is higher.
C)
The experimental and theoretical probability are equal.
Answers
Answer:
A: "The theoretical probability is higher."
Step-by-step explanation:
The theoretical probability of rolling an odd number on a die is 1/2, or 0.5. Since Tami rolled the die 20 times and it landed on an odd number 6 times, the experimental probability of rolling an odd number is 6/20, or 0.3. Since 0.3 is less than 0.5, the theoretical probability is higher. Therefore, the correct answer is option A: "The theoretical probability is higher."
A random group of 114 adults and 136 teenagers completed a maze. Their times were recorded, and a prize was given if they
finished the maze in under 10 minutes.
There were 20 more teenagers than adults that received a prize for completing the maze in under 10 minutes.
There were 62 adults who finished the maze in 10 minutes or longer.
Create a two-way frequency table to represent this data. Type the correct answer in the box. Use numerals instead of words.
Answers
The adults less than 10 minutes are 52, the teenager less than 10 minutes 72, the teenager more than 10 minutes are 64, and the total is 250.
What is mathematical operations in reasoning?
The study is based on the mathematical operations that are multiplication, addition, subtraction, and division. “Mathematical Operations reasoning” is the simple process of the expression of the containing numbers and various operations in the mathematical field.
Time to complete Maze
less than 10 minutes 10 minutes or more Total
Adults 52 62 114
Teenager 72 64 136
Total 124 126 250
114 - 62 = 52 {adults less than 10 minutes}
52 + 20 = 72 {teenager less than 10 minutes}
136 - 72 = 64 {teenager more than 10 minutes}
124 + 126 = 250 {total}
Hence, the adults less than 10 minutes are 52, the teenager less than 10 minutes 72, the teenager more than 10 minutes are 64, and the total is 250.
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