Answers
The area of the given image design is; 15 in²
How to find the area of a triangle?The formula to find the area of a triangle is;
Area = ¹/₂(base * height)
Let us divide the image into two triangles and as such;
Area of biggest triangle = ¹/₂(14 * 15)
= 85 in²
We will now deduct the rectangle that was removed by finding its' area to get;
Area of rectangle = length * width
= 10 * 7 = 70 in²
Thus;
Area of image = 85 - 70
Area of image = 15 in²
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Related Questions
Exercise 2. 5. 2: Proof by contrapositive of statements about integer division. About Prove each statement by contrapositive (a) If x and y are integers such that 3xy then 3x. Solution (b) For any integers x, y, and z, if x|y and xz, then x(y z). (c) If x and y are integers such that x > 1, and x divides y, then x(y 1)
Answers
The statements
(a) If x and y are integers such that 3xy then 3x.
(b) For any integers x, y, and z, if x y and xz, then x(y - z).
(c) If x and y are integers such that x > 1 and if x divides y, then the solution is x(y - 1)
are proved.
The term integers in math is defined as are the collection of whole numbers and negative numbers.
Here we know that x and y are the integers,
Then it takes both positive and negative numbers.
Then we take y=1, then we apply it on the expression then we get,
=> 3x(1) = 3x.
Similarly here we have take that xy|z means xy is a factor of z,
Here we can say xym = z for some integer m.
=> x × ym = z, and ym is an integer by closure hence x is a factor of z such that x|z.
Similarly here we can also y * xm = z, and consider xm is an integer, hence y is a factor of z, i.e. y|z.
Where in the third one, we can take x|y means there exists a constant is written as y = kx
Where as y|x means there exists a constant written as x = cy
When we compare these, then we get,
=> y = kx = kcy
Here we have to true if kc = 1 and since k and c are integers, then we have k = c = 1
Therefore y = kx becomes y = 1*x or y = x
Similarly x = cy becomes x = 1*y or x = y
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there are 14 desktops and 16 laptops what percent of the computers are laptops
Answers
Answer:
53.3%
Step-by-step explanation:
14 + 16 = 30
16/30 x 100 = 53.3% are laptops
You are ask to solve 12x-18 =126
Answers
Add 18 to both sides
12x = 144
Divide by 12 both sides
x = 12
Answer: x = 12
Have a good day ^^
What is ths measure of z. 3
Answers
In 2012, it was estimated that the number of U. S. Households that had dogs as pets was [tex]4. 33 x 10^7[/tex], and the average number of dogs per household was 1. 6. Based on the information, approximately how many dogs were household pets in the U. S. In 2012, in scientific notation?
[tex]2. 71 x 10^7[/tex]
[tex]3. 70 x 10^8[/tex]
[tex]5. 33 x 10^8[/tex]
[tex]6. 93 x 10^7[/tex]
Answers
6.93 × 10⁷ dogs were household pets in the U. S. In 2012.
To find the total number of dogs as household pets in the U.S. in 2012, we need to multiply the number of households by the average number of dogs per household.
Number of households = 4.33 × 10⁷
The average number of dogs per household = 1.6
Total number of dogs = (4.33 x 10⁷) × (1.6) = 6.93 × 10⁷
Therefore, approximately 6.93 × 10⁷ dogs were household pets in the U.S. in 2012.
Hence, the correct answer is D.
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be sure to answer all parts. a small hole in the wing of a space shuttle requires a 21.9 cm2 patch. (a) what is the patch's area in square kilometers (km2)? enter your answer in scientific notation. (b) if the patching material costs nasa $3.91/in2, what is the cost of the patch to the nearest cent?
Answers
(a) The area of the space shuttle is:2.07x10⁻⁹km²
(b) $11.0321 is the cost of the patch.
Area of the patch of the space shuttle = 21.9cm²
a) 1 cm=0.00001 km
1cm²=(0.00001 km)²=10⁻¹⁰km²
21.9cm²=21.9x10⁻¹⁰km²=21.9x10⁻⁹km²
the patch's area =21.9x10⁻⁹km²
b) 1 cm = 0.393701 inch
1cm²=0.1550inch²
21.9cm²=21.9x0.1550inch²=3.3945inch²
The cost of patching area = 3.3945inch²
The cost of patching is are: 3.3945inch²
3.25inch²x3.3945inch²=11.0321
the cost of the patch to the nearest cent=11.0321
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Tyson must complete 30 hours of community service. She does 2 hours each day. Write a liner equation to represent the hours Tyson has left after x days?
Answers
Tyson has (30-2x) hours left after x days .
Linear equation: What is it?A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. (b).
A first-degree polynomial is described as the sum of a collection of terms, each of which is the product of a constant and the first power of a variable in a linear equation.
She works out for two hours per day for a total of x days.
She has thus worked for two hours.
She has 30 hours left to accomplish, of which she has already worked for two of them.
She now has 30 2 hours to finish the task.
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Determine the solution to the following system of linear equations by inspecting the graph below. Enter the solution set as an ordered pair in the form (x,y). If there are no solutions, enter None and enter ALL if there are infinitely many solutions.
Answers
The solution set to the system of linear equations as an ordered pair is (3, -3).
What is a point of intersection?In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines cross each other (intersect), which is represented as an ordered pair containing the point that corresponds to the x-axis and y-axis on a cartesian coordinate.
Note: Each interval on this graph represents 1 unit.
By critically observing the graph of the lines representing the system of linear equations, we can reasonably infer and logically deduce that the correct solution set lies in Quadrant IV and it is denoted by the point of intersection of both the x-coordinate and y-coordinate, which is given by the ordered pair (3, -3).
In conclusion, the ordered pair (3, -3) represents the solution set to the system of linear equations represented by the graph.
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make x the subject for 8x+7=2y-1
Answers
The solution to an inequality is graphed on the number
ne.
-5 -4 -3 -2 -1 0 1 2 3 4 5
Mark this and return
What is another way to represent this solution set?
{xx<4.5}
Ox|x≤4.5}
Oxx> 4.5)
O{x|x24.5)
Save and Exit
Next
Answers
The solution set to the inequality as represented in another way is {x | x ∈ ≤ 4.5}. The second option is correct from the photo.
Representation of sets into a set builder notation:The set builder form is the representation of components of a set by a statement or an expression. The represented element(s) will be written using a variable, accompanied by a vertical line or colon, then the general attribute of the same represented element. This approach avoids listing the elements as seen in the roster method or the listing method.
From the given sets in roster form:
{-5,-4, -3, -2, -1, 0, 1, 2, 3, 4.5}
The same set above can be denoted by x, where x represents all the elements in the set and can be written as:
= {x | x ∈ ≤ 4.5}
This is read as x is an element of x such that x represent all the values from negative infinity to 4.5.
Therefore, we can conclude that the second option is correct from the photo.
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FIELD TRIP A school is planning a field trip to a museum. Tickets cost $4 for students and $8 for adult chaperones. There must be at least 1 adult chaperone for every 9 students and no more than 1 adult Up to 100 people may go on the field trip. chaperone for every 4 students. What is the maximum total cost for tickets?
Answers
Answer:
The maximum total cost for tickets is $320 + $160 = $480.
Step-by-step explanation:
The maximum number of people that can go on the field trip is 100, so the maximum number of students is 100 - (100/5) = 80 students.
The maximum number of adult chaperones is 1 adult chaperone for every 4 students, so the maximum number of chaperones is 80/4 = 20 chaperones.
The total cost for student tickets is $4 x 80 = $320.
The total cost for adult chaperone tickets is $8 x 20 = $160.
The maximum total cost for tickets is $320 + $160 = $480.
Answer:
the maximum amount for the equation is 320+160=480
Sheila collect pokemon card. A of 2018, he ha a Mewtwo card that i twice a old a her Snorlax card. Two year ago, her rare Raichu card wa five time a old a the Snorlax card. If the Raichu card i even year older than the Mewtwo card in what year wa the Raichu card made?
Answers
The Raichu card was made 8 years ago.
To calculate this, we need to take into account the age of the Mewtwo card, the Snorlax card, and the Raichu card.
The Mewtwo card is twice as old as the Snorlax card, so the Mewtwo card is two years old. The Raichu card is five times as old as the Snorlax card, so it must be ten years old.
Since the Raichu card is two years older than the Mewtwo card, it must be eight years old. Therefore, the Raichu card was made eight years ago.
To summarise, the Mewtwo card is two years old, the Snorlax card is one year old, and the Raichu card is ten years old. Therefore, the Raichu card was made eight years ago.
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using the multiple linear regression model you developed in part (a), what is the predicted freshman gpa of bobby engle, a student who has been admitted to ruggles college with a 660 sat score on critical reading and at a 630 sat score on mathematics?
Answers
y= -2.6717 + 0.0043(660) + 0.0045(630) = 3.00 is the GPA Score for Bobby Eagle.
A statistical method known as multiple linear regression (MLR), usually referred to as multiple regression, employs a number of explanatory variables to forecast the result of a response variable. One explanatory variable is used just once in multiple regression, an extension of linear (OLS) regression. Financial and econometric inference both make heavy use of MLR.
Score on critical reading = 660
Score on mathematics = 630
Intercept = -2.6717
Reading(x1) = 0.0043
Mathematics(x2) = 0.0045
Hence, y = -2.6717 + 0.0043(660) + 0.0045(630) is the GPA score for Bobby.
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A man walks due west for 4km. he then changes direction and walks on a bearing of 197 degrees until he is southwest of his starting point. how far is he to the then from his starting point
Answers
Step-by-step explanation:
To solve this problem, we can use the law of cosines. The law of cosines states that for any triangle with sides a, b, and c, and an angle C opposite side c,
c² = a² + b² - 2abcos(C)
In this problem, we can consider the man's starting point as the origin, and the distance he travels in the first leg as the first side of the triangle (a = 4km). The distance he travels in the second leg is the second side of the triangle (b). The angle between the two legs is the angle opposite side c, which is 90 degrees since the man changes direction from due west to southwest.
Therefore, we can use the law of cosines to find the distance he traveled in the second leg:
c² = a² + b² - 2abcos(90)
c² = 4² + b²
c = √(4² + b²)
c = √(16 + b²)
We know that the bearing of the second leg is 197 degrees, which is equivalent to a bearing of -163 degrees, since bearing measurements are taken clockwise from due north.
So we can use the law of cosines to find the distance he traveled in the second leg:
b = √(c² + a² - 2ac cos (-163))
We can now plug in the values we know:
b = √(c² + 4² - 24c*cos(-163))
We can now solve for c:
c = √(b² + 16 - 8bc)
The man is then southwest of his starting point, so the distance from his starting point to the final point is c.
6.4% as a fraction in simplest form
Answers
Answer:32/5
Step-by-step explanation:
32/5
Answer:
Solution: 6.4% as a fraction is 32/5.
Step-by-step explanation:
Harper has $0.70 worth of nickels and dimes. She has 5 more nickels than dimes. By following the steps below, determine the number of nickels, x, and the number of dimes, y, that Harper has.? Determine three ways to have 5 more nickels than dimes
Answers
The number of nickels, x, and the number of dimes y that Harper has are;
8 nickels and 3 dimes
How to solve algebra word problems?From conversion of coins we know that;
1 nickel = $0.05
1 dime = $0.10
Thus, if she has 5 more nickels than dimes, then;
Let x = the number of dimes Harper has
Let x + 5 = the number of nickels Harper has
Thus;
$0.05(x + 5) + $0.10(x) = $0.70
0.05x + 0.25 + 0.10x = 0.70
0.15x = 0.70 - 0.25
0.15x = 0.45
x = 0.45/0.15
x = 3 dimes
Nickels = 8 nickels
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In a group of 60 tudent, 25 play table tenni, 16 do wimming and 22 play cricket, 8 play table tenni and do wimming, 6 play cricket and do wimming, 5 play table tenni and cricket, and 12 tudent do not play any of thee game
Answers
12 students do not play any of the games. Number of students who do not play any of the games = 60 - 82 = 12
A group of 60 students, 25 play table tennis, 16 do swimming and 22 play cricket, 8 play table tennis and do swimming, 6 play cricket and do swimming, 5 play table tennis and cricket.
25 play table tennis
16 do swimming
22 play cricket
8 play table tennis and do swimming
6 play cricket and do swimming
5 play table tennis and cricket
Find the number of students who do not play any of the games
Total number of students = 60
Number of students who play any of the games = 25 + 16 + 22 + 8 + 6 + 5 = 82
Number of students who do not play any of the games = 60 - 82 = 12
12 students do not play any of the games.
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can anyone help me with this?
Answers
$97.056 is the total interest accrued after the first month.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Given, You (or your parents) purchase a new car for $19,725.00 plus 4.75% sales tax. The down payment is $2,175.00 and you (or your parents) have an average credit rating.
The cost of car = 19,725*(1.0475) = 20,661.9375
Down payment = 2,175
So balance amount, P= 20661.9375-2175 = 18,486.9375
So interest for the average rating of a new car = 6.30%
So the interest accrued in first month = 18,486.9375*0.063/12 = $ 97.056
therefore, interest accrued after the first month is $97.056.
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answers
An open circle is at 5 and a bold line starts at 5 and is pointing to the right. Therefore, option B is the correct answer.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality is -3(2x - 5) < 5(2 - x).
Here, -6x+15<10-5x
Add 5x on both the sides of an inequality, we get
-x+15<10
Subtract 15 on both the sides of an inequality, we get
-x<10-15
-x<-5
Multiply -1 on both the sides of an inequality, we get
x>5
Therefore, option B is the correct answer.
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anna leaves her house on her bike traveling at an averge speed of 6 mph. an hour later, her mother sets out after her on the same road, traveling by car. how fast must she drive to reach anna in twn minutes
Answers
The mother must drive at a speed of 6 mph to reach Anna in ten minutes.
To find the speed required for the mother to reach Anna in ten minutes, you need to calculate the distance between them and the time it takes to close the gap.
Let x be the speed of the mother's car in mph.
In one hour, Anna will have covered 6 miles.
In ten minutes, the mother will have covered x * 10/60 miles.
The total distance between them is 6 + x * 10/60 miles.
The mother must cover this distance in ten minutes, so:
x * 10/60 = 6 / (10/60)
x = 6 * (10/60) / (10/60)
x = 6 mph
Therefore, the mother must drive at a speed of 6 mph to reach Anna in ten minutes.
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FInd the simple interest earned on a deposit of $2800 after 5 years at a 2% annual rate.
Answers
The simple interest earned on a deposit of $2800 after 5 years at a 2% annual rate is $280.
What is simple interest?It is the interest calculated on the principal at a given rate for a time period.
We have,
P = $2800
T = 5 years
R = 2%
Now,
The formula for simple interest.
SI = PRT/100
Now,
SI = (2800 x 2 x 5) / 100
SI = 28 x 10
SI = $280
Thus,
Simple interest is $280.
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necesito esto para hoy,porfavor x-3(x+5)=3x+10
Answers
No hay solución para la ecuación algebraica 3 · x + 15 = 3 · x + 10.
¿Cómo resolver una ecuación algebraica?
En este problema tenemos el caso de una ecuación algebraica con una variable única y es nuestra labor determinar su solución, en caso de existir, por métodos algebraicos. Primero, escriba la ecuación algebraica correspondiente:
3 · (x + 5) = 3 · x + 10
Segundo, halle la solución por propiedades algebraicas:
3 · x + 15 = 3 · x + 10
15 = 10 (CRASH!)
La ecuación algebraica 3 · x + 15 = 3 · x + 10 no tiene solución.
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Printing company purchases an ad- vanced color copier/printer for $113,000 After 7 years, the equipment will be obsolete and have no value.
Write a linear equation giving the value of the equipment in terms of the time t
Answers
A linear equation giving the value of the equipment in terms of the time t is calculated to be v = 117000 - 16714.3t.
The value of the colour printer is 117000 $ and machine has no value after 7 years.
As it is given that the machine has no value after 7 years. That mean rate is decreasing every year. So, the decreasing rate is, 117000/7 = 16714.3.
Let us assume v is the value of the machine and t is the time. Then, the linear equation for the given problem is, v = 117000 - 16714.3t
Thus, the required linear equation is v = 117000 - 16714.3t.
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Answer questions 8 and 9.
Find the measure of an arc from the central angle.
Answers
By using the property of measure of an arc from the central angle
m(arc MQN) = 225°
m(arc MPN) = 135°
If m(arc KJH) = 312°
m∠1 = 48°
What is the measure of an arc from the central angle?
The measure of an arc from the central angle is the portion of the circumference of a circle that the arc spans. The measure of an arc is typically given in degrees.
In the given figure
by using the property of measure of an arc from the central angle
m(arc MQN) = 225°
m(arc MPN) = 360° - 225° = 135°
In the second figure,
If m(arc KJH) = 312°
m∠1 = 360° - 312° = 48°
Hence, by using the property of measure of an arc from the central angle
m(arc MQN) = 225°
m(arc MPN) = 135°
If m(arc KJH) = 312°
m∠1 = 48°
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What is the equation of the line that passes through the point (1, 8) and has a slope
of 1?
Answers
Answer:
y = x + 7
Step-by-step explanation:
Equation of line:[tex]\boxed{(y-y_1)=m(x -x_1)}[/tex]
m = 1
(1 , 8) ; x₁ = 1 & y₁= 8;
y - 8 = 1*(x - 1)
y - 8 = x - 1
y = x - 1 + 8
y = x + 7
How many teaspoons are there in 6 milliliters?
Answers
Answer:
70
Step-by-step explanation:
you divide the intergert and div8de its easy
Answer: 70
Step-by-step explanation:
The volume of soda dispensed in a can during production is normally distributed with a mean of 358. 2 ml and a standard deviation of 1. 8 ml. The company does not want more than 2. 5% of all cans to be less than the volume on the label which is 355ml. Is the company meeting its goal? If not, what should the company do? (Show work)
Answers
To meet the goal, the company should adjust the mean and/or standard deviation so that the probability of cans having a volume less than 355ml is less than 2.5%.
A probability is a numerical representation of the likelihood or chance that a specific event will take place.
We can use the z-score formula to find the probability of cans having a volume less than 355 ml.
z-score = (355 - 358.2) / 1.8 = -1.78
Probability of cans having a volume less than 355ml = P(z < -1.78) = 0.0372
The company is not meeting its goal since the probability of cans having a volume less than 355ml is 0.0372 which is greater than 2.5%.
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Quadrilaterals Q and P are similar. What is the scale factor of the dilation that takes P to Q?
A. 3/5
B. 4/5
C. 5/4
D. 5/3
Answers
Answer:
C. 5/4
Step-by-step explanation:
Let s = the scale factor
4s = 5 divide both sides by 4
s = 5/4
mentum.com
Lxpre3310113, 1931
ial Expressions: Mastery Test
5
Drag each tile to the correct box.
Using the order of operations, what are the steps for solving this expression?
40+8+32+(15-7) × 2
Arrange the steps in the order in which they are performed.
3²
5+9
40+8
14+ 16
8x2
KNOW
15-7
Answers
The order in which they performed be
14 + 16 . . . . add 5 + 9
30 . . . . . . . add 14 + 16
What is meant by expression?A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. There are four possible math operations here: addition, subtraction, multiplication, and division.
Given: 40/8 + 3² + (15 - 7) × 2
The order of operations instructs you to begin by assessing parenthesized expressions. This is done by deducting 7 from 15.
40/8 + 3² + 8 × 2 . . . . (15 - 7) = 8
Then you evaluate exponential terms.
40/8 + 9 + 8 × 2 . . . . . 3² = 9
Next, multiply and divide from left to right. In this case, division comes before multiplication.
5 + 9 + 8 × 2 . . . . . divide 40/8 = 5
5 + 9 +16 . . . . . . multiply 8 × 2 = 16
The order in which they performed be
14 + 16 . . . . add 5 + 9
30 . . . . . . . add 14 + 16
The complete question is:
Using the order of operations, what are the steps for solving this expression?
40/8+3^2+(15-7)*2
Arrange the steps in the order in which they are performed.
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In a survey, a group of students were asked to name their favorite world language class. There were 25 students who chose "other" languages. How many students participated? french:42. 5% spanish:45 students participated
Answers
Spanish 45 and french 42.5. When attempting to solve a Venn diagram with three circles, it is best to start by entering the number of items that the three sets of data have in common.
When attempting to solve a Venn diagram with three circles, it is best to start by entering the number of items that the three sets of data have in common. After that, input how many items are still there in each pair of sets' overlapping zone.
The quantity of each set's leftover pieces should be entered. Lastly, locate any missing numbers using any known totals.
Using a Venn diagram to determine probabilities: The Venn diagram's subset's components should be identified. Figure out the subset's frequency. Work out the larger set's overall frequency.
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