Recall that the interior angles of a regular quadrilateral add up to 360 degrees, and a right angle has a measure of 90 degrees.
Let x° be the measure of the fourth angle, then we can set the following equation:
[tex]40^{\circ}+90^{\circ}+90^{\circ}+x^{\circ}=360^{\circ}.[/tex]Adding like terms we get:
[tex]220^{\circ}+x^{\circ}=360^{\circ}.[/tex]Subtracting 220 degrees from the above result we get:
[tex]\begin{gathered} 220^{\circ}+x^{\circ}-220^{\circ}=360^{\circ}-220^{\circ}, \\ x^\circ=140^\circ. \end{gathered}[/tex]Answer:
[tex]140^{\circ}.[/tex]15. The life of a 9-volt battery is normally distributed with a mean of = 2000 hours and a standarddeviation of = 40 hours. What is the proportionof batteries with an average life of 2100 hours ormore? (enter the answer as a percent rounded tothe nearest hundredth as needed)
To answer this question we will use the following formula for the z-score:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma}, \\ where\text{ }x\text{ is the observed value, }\mu\text{ is the mean, and }\sigma\text{ is the standard deviation.} \end{gathered}[/tex]Substituting = 2000h, = 40h and x=2100h we get:
[tex]z=\frac{2100h-2000h}{40h}.[/tex]Simplifying the above result we get:
[tex]z=\frac{100h}{40h}=2.5.[/tex]Using tables we get:
[tex]P(z<2.5)=0.99379[/tex]Then:
[tex]P(z\geq2.5)=1-0.99379=0.00621.[/tex]The above result as a percentage is:
[tex]0.621\%.[/tex]Answer:
[tex]0.62\%.[/tex]
The balance of an account after t years can be found using the expression 4,500(1.75)^t where the initial balance was $4,500. By what percent does the account increase annually?
Solution
The Amount after t years is given by
[tex]A(t)=4500(1.75)^t[/tex]The Percentage annual increase is
[tex]\begin{gathered} \frac{A(1)-A(0)}{A(0)}\times100\% \\ \Rightarrow\frac{4500(1.75)-4500}{4500}\times100\% \\ \Rightarrow0.75\times100\%=75\% \end{gathered}[/tex]Hence, the account increase 75% annually
two friends went to a restaurant and ordered one plain pizza and two sodas. the bill totaled $15.95. later that day, five friends went to the same restaurant. they ordered 3 plain pizzas and 5 sodas. their bill totaled $45.90.write and solve a system of equations to determine the the price of one plain pizza(only an algebraic solution can receive full credit.)
Let:
x = Cost of one plain pizza
y = Cost of one soda
two friends went to a restaurant and ordered one plain pizza and two sodas. the bill totaled $15.95. so:
[tex]\begin{gathered} x+2y=15.95_{\text{ }} \\ \end{gathered}[/tex]later that day, five friends went to the same restaurant. they ordered 3 plain pizzas and 5 sodas. their bill totaled $45.90. so:
[tex]3x+5y=45.90[/tex]Let:
[tex]\begin{gathered} x+2y=15.95_{\text{ }}(1) \\ 3x+5y=45.90_{\text{ }}(2) \end{gathered}[/tex]From (1) solve for x:
[tex]x=15.95-2y_{\text{ }}(3)[/tex]Replace (3) into (2):
[tex]\begin{gathered} 3(15.95-2y)+5y=45.90 \\ 47.85-6y+5y=45.90 \\ -y=-1.95 \\ y=1.95 \end{gathered}[/tex]Replace the value of y into (3):
[tex]\begin{gathered} x=15.95-2(1.95) \\ x=12.05 \end{gathered}[/tex]Therefore, the price of one plain pizza is $12.05
geometry angels.PLS HELP I ONLY HAVE Until 10:00pm on 12/1 then I get a ZERO
We know that the angle 2 and the anlge 4 are equal because of oposite angles so:
[tex]4x-28=3x-9[/tex]and we can solve for x so:
[tex]\begin{gathered} 4x-3x=-9+28 \\ x=19 \end{gathered}[/tex]So:
[tex]\angle2=\angle4=3(19)-9=48º[/tex]Now we also know that angle 1 and 3 are equal and the sum of the internal angles must be:
[tex]\begin{gathered} 360=2(48)+2(y) \\ \frac{360-96}{2}=y \\ y=132 \end{gathered}[/tex]So angle 1 is equal to 132º
help please to find the answer of the blanks
The associated matrix associated to the linear transformation is A = [tex]\left[\begin{array}{cc}5&-6\\1&- 3\\8&- 2\\0 & - 4\end{array}\right][/tex].
How to find the associated matrix associated to a linear transformation
Linear transformations are applications between two vector spaces that preserves the properties of vector addition and the product of a vector and a scalar. In this problem, we find the following linear transformation between the two bases:
W → V
(w₁, w₂, w₃, w₄) → v₁
Then, there is the following relationship:
V = A · W
Where A is the associated matrix. The matrix V has four rows and one column and the matrix W has two rows and one column. Then, by property of multiplication of matrices, the associated matrix has four rows and two columns. Then, the associated matrix is:
A = [tex]\left[\begin{array}{cc}5&-6\\1&- 3\\8&- 2\\0 & - 4\end{array}\right][/tex]
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Find the value of f(4) for the func
f(x) = -3(x + 2)
f(4) = (Simplify your answer.)
Answer: f(4) = -18
Step-by-step explanation:
f(4) = -3(4 + 2)
= -3(6)
= -18
lan and Matthew went shopping. lan spent $20 less than twice as much as Matthew spent. In total, they spent $130.
Using linear algebra, we concluded, the Mathew spent $50 and lan spent $80
What is Linear Algebra?
Vectors, matrices, vector spaces, and linear transformations are all topics covered in the mathematical field of linear algebra. Linear algebra is much better understood than other areas of mathematics, which are regularly stimulated by novel concepts and unresolved issues.
According to the question,
Let Mathew spent $x
lan spent = 2x - 20
Total money spent = $130
⇒ 2x - 20 + x = 130
⇒ 3x - 20 = 130
⇒ 3x = 150
⇒ x = 50
2x - 20 = 2(50) - 20
= 80
So, Mathew spent $50 and lan spent $80
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PLS HELP ME ASAP!!!!
The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does.
What is meant by data set?A data set is a group of figures or values related to a specific topic. a list of words, numbers, or symbols, the values of which are frequently the outcomes of an investigation or observation. There are typically multiple variables in data sets.
A dataset is an organized group of data typically connected to a certain body of work. An organized collection of data kept as several datasets is called a database.
In an ordered data set, the median is the value in the middle. The mean is calculated by dividing the sum of all values by the total number of values. The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does.
Therefore, the correct answer is option c) The northbound cars were generally faster because the median for the northbound cars is greater than the median for the southbound cars.
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The density of copper is 9.86 g/cm".
Work out the mass of the solid copper cuboid in kg
10 cm
3 cm
5 cm
Step by step
10x3 thousands=?How many thousands are in the answer?
Given:
[tex]10\times3\text{ thousands}[/tex]Required:
We need to find the number of thousands.
Explanation:
Multiply 10 and 3.
[tex]10\times3\text{ =30}[/tex][tex]10\times3\text{ thousands=30 thousands}[/tex]The number of thousands is 30.
Final answer:
There are 30 thousands.
Vector A and B are at right angles and have the same initial point. Find the magnitude and direction from vector A of the resultant vector.
We need to find the magnitude and direction from vector A of the resultanr vector.
The box and whisker plot summarizes the data collected on the number of Broadway tickets sold and the actual number of attendees at the plays. Which statement is TRUE about the statistics?
A.) The majority of the data values fall in the upper quartile for both sets of data.
B.) There were fewer tickets purchased than people attending the plays.
C.) The medians of the populations are the same.
D.) There were fewer attendees than purchased tickets.
The plot:
The true statement based on the information is that D. There were fewer attendees than purchased tickets.
Whet is a box and whisker plot?A box and whisker plot is a graphical representation of variance in a set of data. A histogram analysis is sufficient in most circumstances, but a box and whisker plot can provide more detail while allowing different sets of data to be displayed in the same graph.
The box and whisker figure highlights data on the number of Broadway tickets sold and actual attendance at the performances. In this case, the graph shows that the number of tickets are more.
Therefore, the correct option is D.
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4. Answer the following questions based on the information below:Han wants to build a dog house. He makes a list of the materials needed:• At least 60 square feet of plywood for the surfaces• At least 36 feet of wood planks for the frame of the dog house• Between 1 and 2 quarts of paintHan's budget is $65. Plywood costs $0.70 per square foot, planks of wood cost $0.10 per foot, andpaint costs $8 per quart.
Part A
The variable are;
Plywood, wood planks, quarts of paint
Part B
Let p represent Plywood
Let w represent Plank of wood
[tex]1Part c
Let p represent Plywood
Let w represent Plank of wood
Let q represent quarts of paint
[tex]0.7p+0.1w+8q\leq65[/tex]wildlife shelter in North Carolina is home to native species of birds. mammals, and reptiles. If cat chow is sold in 20 lb bags, what is the least number of bags of cat chow needed for one year at this shelter
At least 26 bags of cat chow is required for a period of one year to fulfil the demand at the wildlife shelter in North Carolina
Quantity of cat chow sold in each bag = 20 lb
Consumption in lb of cat chow per week in the wildlife shelter = 10 lb
Number of weeks in a year = 52 weeks
The total quantity of cat chow required for 52 weeks = Weekly consumption of cat chow*Number of weeks
= 10*52
= 520 lb
Number of bags required = Toal quantity of cat chow required for 52 weeks/ Quantity of cat chow sold in each bag
= 520/20
= 26 bags
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use basic trigonometric identities to simplify the expression: sin^3 (x) + cos^2 (x) sin (x)
Given the following trigonometric expression:
[tex]sin^3x+cos^2x*sinx=?[/tex]We will simplify the expression as follows:
First, taking sin (x) as a common
[tex]=sin\text{ }x*(sin^2x+cos^2x)[/tex]Second, we will use the following trigonometric identity:
[tex]sin^2x+cos^2x=1\rightarrow(1)[/tex]Finally, substitute the trigonometric identity number (1) into the given expression
[tex]=sin\text{ }x*1=sin\text{ }x[/tex]So, the answer will be sin (x)
Hello I need help on this math questionYou can zoom in the picture
In this problem, we have the transformation
A(-3,4) -------> A'(-15,20)
so
The rule is
(x,y) -----> (5x,5y)
the answer is option b
What is 30 percent of 120?
Answer:
30 percent of 120 is 36
How would I multiply these two exponents?
The first step when multiplying fractions is to multiply the two numerators. The second step is to multiply the two denominators. Finally, simplify the new fractions. The fractions can also be simplified before multiplying by factoring out common factors in the numerator and denominator.
M={z / z is an integer and -2
The given set in roster method is written as {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}.
Given that, M={x : x is an integer and 2 ≤ x ≤20.
What is roster method?The roster method is defined as a way to show the elements of a set by listing the elements inside of brackets.
Now, the given set in roster method can be written as follows:
{2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}
Therefore, the given set in roster method is written as {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}.
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"Your question is incomplete, probably the complete question/missing part is:"
Write the given set in roster method: M={x : x is an integer and 2 ≤ x ≤20
The area of a window measures 336 Square inches. If the window is 16 inches wide. How long is the window?
The window has a length of 21 inches
How to determine the length of the window?From the question, we have the following parameters
Area of the window = 336 square inches
Width of the window = 16 inches
The area of the window is the product of its dimensions
So, we have
Area = Width of the window x Length of the window
Substitute the known values in the above equation
So, we have the following equation
336 = 16 * Length
Divide both sides by 16
Length = 21
Hence, the length is 21 inches
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Identify the reasoning that would justify each step in solving for m
Given
[tex]\frac{3}{4}(m-500)=8000+4000[/tex]Notice that the right side of the equation consists of like terms (they do not depend on m). Therefore, Step 1 goes with Combine like terms.
Then,
[tex]\frac{3}{4}(m-500)=\frac{3}{4}*m+\frac{3}{5}(-500)=\frac{3m}{4}-375\rightarrow\text{ distributive property}[/tex]Step 2 applies the distributive property.
As for the properties of the equality,
[tex]\begin{gathered} a=b\Rightarrow a+c=b+c\rightarrow\text{ addition property of equality} \\ a=b\Rightarrow ac=bc\rightarrow\text{ multiplication property of equality\rbrack} \\ a=b\Rightarrow\frac{a}{c}=\frac{b}{c}\rightarrow\text{ division property of inequality} \end{gathered}[/tex]Thus, steps 3 through 5 are:
Step 3 - Addition property
Step 4 - Division property
Step 5 - Multiplication property
1. What is the reciprocal of 5? 6 Show your work below! (click "Show Work Type a response OD
Answer:
1/5
Step-by-step explanation:
a reciprocal is the multiplicative inverse
Answer:
The reciprocal of 5 is 1/5
Step-by-step explanation:
The reciprocal of a number is the fraction flipped upside down
6/1 = 1/6
⇒ 5/1 = 1/5
Name the point that lies on this line: y = 2 + 5(x + 7)
(1, 42)
1) Since we have an equation of the line y = 2 + 5(x + 7) let's find one point that ∈ to this line.
2) Let's plug into that for x, the value of x=1
y= 2+ 5(1+7)
y= 2 +5(8)
y= 2 +40
y= 42
3) So one of the points that lie on this line is (1, 42) i.e. belong to that line.
A player hit a baseball from home plate 3 feet above the ground. The graph shows the height in feet of the baseball above the grounds as a quadratic function of x, the horizontal distance in feet of the baseball from home plate.What is the domain of this function?3≤x≤400≤y≤103≤y≤100≤x≤40
As the image attached shows, the horizontal distance reached by the ball is 40 feet.
Notice that the horizontal movement goes from 0 to 40, this means the domain is
[tex]0\leq x\leq40[/tex]Since x-values are domain values.
Therefore, the right answer is the last choice.i need help asp ;-;
Which of the following values is less than −|58|?
A. −48
B. 68
C. −68
D. 48
Answer:
C. -68
Step-by-step explanation:
Using absolute value symbols, it makes any negative number a positive. But, the negative sign is outside the absolute value signs, making the number -58. -68 is the only number less than -58.
if y =3x^3 + 2x^2 - 5x + 2, find d^3y/dx^3
Answer:
18
Step-by-Step Explanation:
[tex]\frac{dy}{dx}=9x^2 + 4x-5 \\ \\ \frac{d^2 y}{dx^2}=18x+4 \\ \\ \frac{d^3 y}{dx^3}=18[/tex]
Given: Ray BD bisects prove: <1 and <3 are supplementary
Let's begin by listing out the information given to us:
[tex]\begin{gathered} |BD|\text{ bisects }|EBC|\text{ into equal parts}\Rightarrow\angle1=\angle2 \\ \angle2\text{ is supplementary with }\angle3;\angle2+\angle3=180^{\circ} \\ \therefore\angle1+\angle3=180^{\circ} \end{gathered}[/tex]Describe a situation that can be modeled using the given simulation. 1 marble chosen from a bag containing 11 red marbles and 4 blue marbles a. Determine the probability of selecting a month from January through November and the month begins with the letter J. b. Determine the probability of surveying 11 people and 4 of them like playing checkers. c. Determine the probability of selecting a pair of tennis shoes from a shoe collection that contains 4 dress shoes and 7 tennis shoes. d. Determine the probability of selecting an apple from a basket that contains 11 apples and 4 oranges.
Answer:
Explanation:
A bag contains 11 red marbles and 4 blue marbles.
• The total number of marbles = 11+4=15
1 marble of any color is chosen random from the bag with a probability of 1/15.
A situation that can be modeled using such a situation must be one that also has a probability of 1/15.
In Option D,
In August, a giant panda named Lucky was born at the Silver City Zoo. In September, Lucky
weighed 3.07 pounds. Today, Lucky is weighed again and he is heavier than before. Now
Lucky weighs 10.81 pounds.
Use an equation to find the amount of weight Lucky gained between September and today.
Using linear equations, the amount of weight Lucky gained between September and today is 7.74 pounds.
What is a Linear equation?An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. The standard form of a linear equation in one variable is the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.So, in September, Lucky weighed = 3.07 pounds
Today's Lucky weighed = 10.81 poundsThe equation form is:
Let x = weight to find Lucky3.07 + x = 10.81This is a linear equationSo, now solve this linear equation and find 'x' as follows:
3.07 + x = 10.81=> x = 10.81 - 3.07=> x = 7.74Therefore, using linear equations, the amount of weight Lucky gained between September and today is 7.74 pounds.
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a real life situation for -2 × 4
How many miles of gas does my car travel if it used 2 gallons of gas with a speed of 4 mi/h?