The ordered pair for point H would be (-9,8).
What is graph?Graph is a mathematical structure used to model pairwise relations between objects. It consists of a set of nodes, which represent the objects, and a set of edges, which represent the relations between pairs of objects. Graphs can be used to represent networks, flows, and even data structures such as trees or linked lists. They are also used in various optimisation problems, such as route finding and scheduling.
The correct answer is B) (-9,8). To find the location of point H, Jessica needs to move 5 units to the left on the x-axis, which would put it at -9. She then needs to move 5 units up on the y-axis, which would put it at 8. Therefore, the ordered pair for point H would be (-9,8).
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The ordered pair for point H would be (-9,8).
What is graph?Graph is a mathematical structure used to model pairwise relations between objects. It consists of a set of nodes, which represent the objects, and a set of edges, which represent the relations between pairs of objects.
The correct answer is B) (-9,8). To find the ordered pair for point H, you need to add 5 units to the x-coordinate of point G, and 5 units to the y-coordinate of point G. Since the x-coordinate of point G is -4 and the y-coordinate of point G is 3, the x-coordinate of point H would be -4 + 5 = -9 and the y-coordinate of point H would be 3 + 5 = 8. Therefore, the ordered pair for point H would be (-9,8).
The correct answer is B) (-9,8). To find the location of point H, Jessica needs to move 5 units to the left on the x-axis, which would put it at -9.
She then needs to move 5 units up on the y-axis, which would put it at 8. Therefore, the ordered pair for point H would be (-9,8).
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the prescriber orders medication f 150 mcg po q.12h. the pharmacy sends a bottle labeled: medication f 0.05 mg/ml. how many milliliters will the nurse administer with each dose?
The nurse will have to administer 3 milliliters with each dose.
When the prescriber orders medication f 150 mcg po q.12h, the pharmacy sends a bottle labeled:
medication f 0.05 mg/ml.
Milliliters will the nurse administer with each dose :
The conversion factor from mcg to mg is 1/1000.
Therefore, 150 mcg = 150/1000 = 0.15 mg.
The nurse has to administer 0.15 mg of medication f per dose.
The medication f available with the pharmacy is 0.05 mg/ml.
So, the nurse has to administer 0.15 mg in a single dose, which is equal to three times the quantity of medication f available in the bottle (0.05 mg/ml).
Therefore, the nurse has to administer 3 ml (0.05 mg/ml × 3 ml) of medication f with each dose.
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5. Diego is building a fence for a rectangular garden. It needs to be at least 10 feet
wide and at least 8 feet long. The fencing he uses costs $3 per foot. His budget is
$120. He wrote some inequalities to represent the constraints in this situation:
1) f = 2x + 2y
2) x ≥ 10
3) y ≥ 8
4) 3f ≤ 120
a. Explain what each equation or inequality represents.
Directions: Illustrate and solve the following problems:
1. Two consecutive sides of a parallelogram measure 4 m and 9 m,
respectively. What is the perimeter of the parallelogram?
2.One diagonal of a square measure (2x + 4) in. If the other diagonal
measures 16 in, what is x?
3.Given trapezoid QRST with QR//TS and UV as the median. If mQR = 12cm and mUV = 24 cm, what is mUV?
4.An isosceles trapezoid with a diagonal that measures 42 cm and one legmeasures 23 cm. What is the length of the other diagonal?
5.Given kite HOPE with diagonals mHP = 10 cm and m0E = 18 cm. What isthe area of the kite?
Answer:
1. The perimeter of a parallelogram is the sum of the lengths of all four sides. If two consecutive sides of a parallelogram measure 4 m and 9 m, respectively, then the other two sides must also measure 4 m and 9 m, respectively (since opposite sides of a parallelogram are equal in length). Therefore, the perimeter of the parallelogram is:
Perimeter = 4 m + 9 m + 4 m + 9 m = 26 m
So the perimeter of the parallelogram is 26 meters.
2. In a square, both diagonals are equal in length. If one diagonal measures (2x + 4) in and the other diagonal measures 16 in, then we can write:
2x + 4 = 16
Solving for x, we get:
x = 6
So the value of x is 6 inches.
3. In a trapezoid, the length of the median is equal to the average of the lengths of the two parallel sides. If QR is parallel to TS and mQR = 12 cm, then mTS must also be equal to 12 cm. Let x be the length of the base of the trapezoid.
Then, we have:
mUV = (mQR + mTS)/2
Substituting the given values, we get:
24 cm = (12 cm + 12 cm + x)/2
Simplifying, we get:
24 cm = (24 cm + x)/2
Multiplying both sides by 2, we get:
48 cm = 24 cm + x
Subtracting 24 cm from both sides, we get:
x = 24 cm
So the length of the base of the trapezoid is 24 cm, and the length of the median UV is 24 cm.
(If this isn't right, I'm sorry!)
4. In an isosceles trapezoid, the diagonals are equal in length. If one diagonal measures 42 cm and one leg measures 23 cm, then we can use the Pythagorean theorem to find the length of the other leg:
d^2 = l^2 + (b/2)^2
where d is the length of the diagonal, l is the length of each leg, and b is the length of the base. Substituting the given values, we get:
42^2 = 23^2 + (b/2)^2
Simplifying, we get:
b^2/4 = 42^2 - 23^2
b^2/4 = 1253
Multiplying both sides by 4, we get:
b^2 = 5012
Taking the square root of both sides, we get:
b = sqrt(5012) ≈ 70.77
So the length of the other diagonal is also 42 cm.
5. The area of a kite is equal to half the product of the lengths of its diagonals. If mHP = 10 cm and mOE = 18 cm, then we can write:
Area = (mHP x mOE)/2
Substituting the given values, we get:
Area = (10 cm x 18 cm)/2 = 90 cm^2
So the area of the kite is 90 square centimeters.
I hope this helps! I'm sorry if this was wrong. If you need more help, ask me! :]
The following table shows the dirstribution of marks in mathematics
Marks (less than) No.of students
10 7
20 28
30 54
40 71
50 84
60 105
70 147
80 180
With the help of the graph paper, taking 2cm=10units
along one axis and 2cm=20units along the other axis, plot an ogive for the above distribution and use it to find the
a)Median
b)Number of students who scared distinction marks (75% and above)
c)Number of students who passed the examination if pass mark is 35%
The number of students who passed the examination is 152.
How to solveGiven: Marks distribution in Mathematics
To Find: Plot an ogive, the median, the number of students who scored distinction marks (75% and above), and the number of students who passed the examination if the pass marks are 35%.
Solution:
Marks Number of students
Less than 10 7
Less than 20 28
Less than 30 54
Less than 40 71
Less than 50 84
Less than 60 105
Less than 70 147
Less than 80 180
Ogive:
An ogive is a graph that represents the cumulative frequency distribution of a set of data. To plot an ogive, we plot the upper limits of each class on the x-axis and the corresponding cumulative frequency on the y-axis. We then join the points with a free-hand smooth curve to obtain the ogive.
Median:
To find the median from the graph, we draw a line from the value of 50 on the y-axis to the ogive curve and then drop it down to the x-axis. The point where the line intersects the x-axis gives us the median. In this case, the approximate median value from the graph is 52.
The number of students who scored distinction marks:
To find the number of students who scored distinction marks (75% and above), we first calculate 75% of the total number of students, which is 0.75 x 180 = 135.
From the ogive graph, we see that the number of students who scored less than 75% marks is 105.
Therefore, the number of students who scored 75% or more marks is 180 - 105 = 75.
The number of students who passed the examination:
To find the number of students who passed the examination if the pass marks are 35%, we first calculate 35% of the total number of students, which is 0.35 x 180 = 63.
From the ogive graph, we see that the number of students who scored less than 35% marks is 28.
Therefore, the number of students who passed the examination is 180 - 28 = 152.
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12.5 points
Question at position 4
Marcus has a circuit that uses a battery to light up a light bulb. He needs three wires to make his circuit. He changes the circuit to have a paper clip attached to wire 2 as shown in the picture below.
Marcus has a circuit that uses a battery to light up a light bulb. He needs three wires to make his circuit. He changes the circuit to have a paper clip attached to wire 2 as shown in the picture below.
A. The battery will die.
B. The light bulb will light up.
C. The light bulb will break.
D. The paper clip will turn black.
Answer:
B
Step-by-step explanation:
the metal is a conductor
st Common Factor and Factoring Find the greatest common factor for the list of monomials. x^(3)y^(5)z^(3),y^(3)z^(3),xy^(3)z^(2) The GCF is
[tex]y^(3)z^(2)[/tex] is the greatest common factor for the given set of monomials.
The highest power of each variable that is shared by all of the given monomials must be identified in order to calculate the greatest common factor (GCF) for the given list of monomials. To put it another way, we must first determine the prime factors of each monomial before determining the factors that are shared by all the monomials.
Prime factorization for each monomial:
[tex]x^(3)y^(5)z^(3) = (x * x * x) * (y * y * y * y * y) * (z * z * z)y^(3)z^(3) = (y * y * y) * (z * z * z)xy^(3)z^(2) = (x) * (y * y * y) * (z * z)[/tex]
Factors are common to all monomials are [tex]y^(3), z^(2)[/tex]. The GCF is [tex]y^(3)z^(2)[/tex].
This is appropriate GCF by dividing each monomial by [tex]y^(3)z^(2)[/tex] and verify that result is whole number. For eg:
[tex]x^(3)y^(5)z^(3) / (y^(3)z^(2)) = x^(3)y^(2)zy^(3)z^(3) / (y^(3)z^(2)) = yzxy^(3)z^(2) / (y^(3)z^(2)) = x/y[/tex]
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Find the surface area of water tower that is 40 feet tall and has a diameter of 30 feet. DO NOT ROUND YOUR ANSWER!
Answer: SA=5183.62788
Step-by-step explanation:
A=2πrh+2πr2=2·π·15·40+2·π·152≈ 5183.62788
~Find the radius- 30 divided by 2= 15 so radius =15
When the litres are 16 how many litres are 3/4 of the tank capacity?
Answer:
16 litres = 100% of the tank capacity
x litres = 75% of the tank capacity (since 3/4 is equivalent to 75%)
To solve for x, we can cross-multiply and simplify:
16 * 75 = 100x
1200 = 100x
x = 12
Therefore, 3/4 of the tank capacity when the tank holds 16 litres is 12 litres.
Answer:
= 12 liters.
Step-by-step explanation:
16*3/4 =48/4.
= 12
Please help will mark brainliest please!!!
Answer: Find the square root of 60i-11
Step-by-step explanation:
i is imaginary number
you can't find the square root of i because i is an imaginary number unless you put sqrt(i)
A box has a base area of 1.1 m2.
The box is placed on the ground and exerts a force of 4.5 kN.
What pressure is the force applied with?
Give your answer in kN/m2 and rounded to 2 dp.
Answer:
To find the pressure that the box exerts on the ground, we need to divide the force by the area of the base:
pressure = force / area
We are given that the force is 4.5 kN and the area is 1.1 m². However, we need to convert the force from kilonewtons to newtons before we can divide by the area:
force = 4.5 kN = 4,500 N
Now we can plug in the values:
pressure = 4,500 N / 1.1 m² = 4,090.91 N/m²
To express the pressure in kilonewtons per square meter, we need to divide by 1,000:
pressure = 4.09091 kN/m²
Rounding to 2 decimal places, we get:
pressure ≈ 4.09 kN/m²
Therefore, the pressure exerted by the box on the ground is approximately 4.09 kN/m².
Find the angle of elevation that a 30-foot ladder, leaning against a wall, if the bottom
of the ladder is 9 feet from the base of the wall.
Answer:
Step-by-step explanation:
Question 4, please help
4/10
Option (a) is correct Mr. Reynolds walks 2000 feet per minute for 8 minute. Here it is the condition of speed.
What is Speed?Speed is define as the distance covered by a person in a given interval or time. It is generally denotes in Km/h or m/sec.
[tex]Speed\ (S)= Distance\ (d) * Time\ (t)[/tex]
Distance, It is an area cover by a person to complete his journey.
Distance is generally denoted by km, m etc,
Time, It is an interval in which generally person complete it task.
It is generally denoted by hour (h), Minute (min) or Second (Sec).
The correct is (a) Mr. Reynolds walks 2000 feet per minute for 8 minute. Here it is the condition of speed.
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The quantity y varies directly with the square of x and inversely with z. When x is 9 and z is 27, y is 6. What is the constant of variation?
2
9
18
54
y varies directly as x means
[tex]y=kx[/tex]
y varies inversely with z means
[tex]y=k\div z[/tex]
therefore
[tex]y=(kx^2)\div z[/tex]
k=constant of variation
[tex]6=(k9^2)\div 27[/tex]
[tex]6=(k81)\div27[/tex]
[tex]6=3k[/tex]
divide both sides by 3
[tex]2=k[/tex]
the constant of variation is 2
If the quantity y varies directly with the square of x and inversely with z, then we can write the following equation:
What is equation ?
A assertion that two mathematical expressions are equal is known as an equation. It typically consists of variables, constants, and mathematical operations, and it may also include functions, exponents, and other mathematical symbols. Equations are used to represent relationships between quantities in mathematics and to solve problems in various fields such as physics, engineering, and economics.
y = k * (x^2) / z
where k is the constant of variation.
We are given that when x is 9, z is 27, and y is 6. Substituting these values into the equation, we get:
6 = k * (9^2) / 27
Simplifying, we get:
6 = k * 3
k = 6 / 3
k = 2
Therefore, the constant of variation is 2.
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A textbook store sold a combined total of 288 history and chemistry textbooks in a week. The number of chemistry textbooks sold was 72 less than the number of history textbooks sold. How many textbooks of each type were sold?
The number οf histοry bοοks is 180 that sοld in a week. The number οf chemistry textbοοks is 108 sοld in a week.
What is an equatiοn?There are many different ways tο define an equatiοn. The definitiοn οf an equatiοn in algebra is a mathematical declaratiοn that illustrates the equality οf twο mathematical expressiοns.
Given that the tοtal number οf bοοks that sοld in a week is 288.
The number οf chemistry textbοοks sοld was 72 less than the number οf histοry textbοοks sοld.
Assume that the number οf histοry textbοοks sοld was x.
The number οf chemistry textbοοks sοld was (x-72)
The tοtal number οf bοοks sοld was x + (x-72) = 2x - 72.
Accοrding tο the questiοn:
2x - 72 = 288
Add 72 frοm bοth sides:
2x - 72 + 72 = 288 + 72
2x = 360
Divide bοth sides by 2:
x = 360/2
x = 180
The number οf histοry textbοοks sοld was 180.
The number οf chemistry textbοοks sοld was (180-72) = 108.
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A carpet is placed in the middle of a room 15m long and 12m broad so that it leaves a uniform width of 1m around it . find the area and the cost of the carpet at Rupee 500 square meter
Answer:
[tex]130m^{2}[/tex] , [tex]65.000 rs[/tex]
Step-by-step explanation:
Given Length = 15m
Given Breadth = 12m
Since there is a 1m gap between the sides,
Actual Length = 15 - 2 = 13m
Actual Breadth = 12 - 2 = 10m
From here find the Area:
L * B = AR of a cuboid , so
13 x 10 = [tex]130m^{2}[/tex] is the Area
for every [tex]m^{2}[/tex] it is 500 rupees, so for [tex]130m^{2}[/tex] ,
130 * 500 = 65,000 rupees.
Here is a diagram of a person standing next to a lorry.
The diagram shows two centimetre rulers.
The person and the lorry are drawn to the same scale.
The lorry is approximately 11.2 m in length.
Using the scale diagram, estimate the height of the person in metres.
By using the scale diagram, the height of this person in meters is equal to 1.6 meter.
What is scale factor?In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):
Scale factor = Dimension of image (new figure)/Dimension of pre-image(actual figure)
Based on the information provided about the lorry, the lorry is approximately 11.2 m in length and 14 cm on a scale diagram. Therefore, the height of the person in meters can be calculated as follows;
1 centimeter = 11.2/14
1 centimeter = 0.8 meter.
Height of the person in meters = 0.8 meter × 2
Height of the person in meters = 1.6 meter.
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A graph comparing the points (x) to the amount of money earned (y) in a minor football league is given by y=200x+500. What is the gradient?
The gradient of the line is 200, hence that is the answer.
What does the word "point" actually mean?
A point is a dot on a sheet of paper or in a plane. There are no lengths, widths, or heights in a point. It establishes a plane's position or location. To make a point, mark a dot on a piece of paper with an A or another capital letter.
The slope-intercept version of the equations y = 200x + 500 is y = mx + b, wherein m is the line's gradient and b is its y-intercept.
The value of x, which really is 200, acts as the gradient (or gradient) in this equation. As a result, the line's gradient is 200.
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One face of a cube shaped Paco has an area of 7.6 square inches. What is the lateral surface area of the package
The lateral surface area of the cube shaped Paco is 45.6 square inches.
What is the lateral surface area of cube shape?In a cube, all six faces are identical squares, so there is no distinction between the lateral surface area and the total surface area. The surface area of a cube can be found by adding up the areas of all six faces.
If s represents the length of each edge of the cube, then the surface area S can be calculated using the formula: S = 6s²
So the lateral surface area of a cube with edge length s is simply 6 times the area of one of its faces, which is just the area of a square with side length s.
The Lateral surface area of a cube = 6s²
or we can say that, Lateral surface area = 6×(area of one face of a cube)
Given that the area of one face of a cube shaped Paco is 7.6 square inches.
Lateral surface area = 6×(7.6) = 45.6 square inches
Therefore, the lateral surface area of the cube shaped Paco is 45.6 square inches.
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PLEASE HELP!!!!!!!!!!!!
Answer: 6
Step-by-step explanation:
When x=-3, y=6
You can count it, 1,2,3,4,5,6.
Hope you found that helpful!
How to write the correct solution of 5a^2-25b^×
The correct solution of the expression 5a² -25bˣ is 5(a² - 5bˣ)
How to determine the correct solution of the expressionFrom the question, we have the following parameters that can be used in our computation:
5a² -25bˣ
The expression is already in its simplest form in terms of combining like terms.
However, we can still look into factoring the expression
To do this, we can factor out the greatest common factor of 5 and rewrite the expression as follows:
5a² -25bˣ = 5(a² - 5bˣ)
This is the factored form of the expression, where the greatest common factor of 5 has been factored out.
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what is −4y−4+(−3)? kkkxznkk;mxk;mxck;mk;mk;xc
Answer:
-4y-7
Step-by-step explanation:
- 4 y - 4 + ( - 3 )
We keep the -4y as it is since it can not be simplified. Then we try to open the parentheses. we do this by multiplying by 1.
- 4 y - 4 + 1 * ( - 3)
= - 4 y - 4 - 3
Then we combine the - 4 and -3.
= - 4 y - 7
Answer: I can confirm that it is '-4y-7'
Step-by-step explanation:
find the probability of selecting a black checker from a bag of 6 black and 4 red checkers, replacing it and selecting another black
The probability of selecting a black checker from a bag of 6 black and 4 red checkers, replacing it, and selecting another black is 9/25.
To find the probability follow these-
Determine the probability of selecting a black checker on the first draw.
There are 6 black checkers and a total of 10 checkers (6 black + 4 red).
So, the probability of selecting a black checker on the first draw is 6/10,
which can be simplified to 3/5.
Since the black checker is replaced, there are still 6 black checkers and
a total of 10 checkers in the bag. Therefore, the probability of selecting a
black checker on the second draw is also 3/5.
To find the probability of both events occurring, multiply the probabilities together: (3/5) × (3/5) = 9/25.
So, the probability of selecting a black checker from a bag of 6 black and
4 red checkers, replacing it, and selecting another black is 9/25.
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PLEASE HELP THANK YOU The cuboid-shaped container below is partly filled with water. What percentage of the container is filled with water? Give your answer to 1 d.p. please see attachment!
Answer:
The volume of the container is 1872 cubic cm. The volume of the water is 672 cubic cm.
Therefore, 672/1872 = 0.36 or 36%
The tree diagram shows the sample space of two-digit numbers that can be created using the digits 7,1 ,9 and 4. What is the probability of choosing a number from the sample space that contains 1 or 4 ?
The prοbability οf chοοsing a number frοm the sample space that cοntains 1 οr 4 is 1/2.
What is prοbability ?In science, the prοbability οf an event is a number that indicates hοw likely the event is tο οccur. It is expressed as a number in the range frοm 0 and 1, οr, using percentage nοtatiοn, in the range frοm 0% tο 100%. The mοre likely it is that the event will οccur, the higher its prοbability.
space οf twο-digit numbers that can be created using the digits 7,1 ,9 and 4. What is the prοbability οf chοοsing a number frοm the sample space that cοntains 1 οr 4 ?
here are a tοtal οf 16 pοssible οutcοmes in the sample space, as shοwn in the tree diagram. Out οf these 16 pοssible οutcοmes, 8 οf them cοntain the digit 1 οr 4 (i.e., 14, 17, 19, 41, 44, 71, 74, 91).
Therefοre, the prοbability οf chοοsing a number frοm the sample space that cοntains 1 οr 4 is:
P(1 οr 4) = 8/16 = 1/2
Sο the prοbability is 1/2.
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How much is the allowed housing expense for the yr if u earn 53698. 00 a yr?
The allowed housing expense for the year is $38,582.01.
The minimum realized income per month is $1,774.53.
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”.
1 ) p = 7.65 + 11.5 + 9 = 28.15 %
$53,698.00 · ( 1 - 0.2815 ) =
= $53,698.00 · 0.7185 = $38,582.01
The allowed housing expense for the year is $38,582.01.
2 ) $1,275.00 : 0.7185 = $1,774.53
The minimum realized income per month is $1,774.53.
The complete question is-
1.) You (or your parents) earn $53,698.00/yr and you have deductions of FICA (7.65%), federal tax withholding (11.5%), and state tax withholding (9%). How much is the allowed housing expense for the year? (1 point)
$ /year
2.) You (or your parents) plan to pay $1,275.00/month for a mortgage. How much is the minimum realized income per month to the nearest penny
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Un niño está haciendo volar dos cometas al mismo tiempo; tiene 380 pies de cuerda a una de las cometas y 420 pies para la otra. Él estima que el ángulo entre las dos cuerdas es de 30°. Aproxime la distancia entre las cometas.
Podemos utilizar la ley de cosenos para aproximar la distancia entre las cometas. Primero, necesitamos encontrar la longitud de la tercera cuerda, que conecta los puntos donde se cruzan las dos cuerdas que sostienen las cometas. Podemos usar trigonometría para encontrar la altura de este triángulo.
El ángulo opuesto a la altura es de 30°, por lo que podemos calcular la altura como:
sin(30°) = altura / 200altura = 100 piesAhora podemos usar la ley de cosenos para encontrar la longitud de la tercera cuerda:
d^2 = 380^2 + 420^2 - 2(380)(420)cos(30°)d^2 = 144400d ≈ 380 piesEntonces, la distancia entre las cometas es aproximadamente de 380 pies.
HELP PLEASE THIS WAS DUE YESTERDAY
MONEY Hans opens a savings account by depositing $1200. The account earns 0.2 percent interest compounded weekly. How much will be in the account in 10 years if he makes no more deposits? Assume that there are exactly 52 weeks in a year, and round your answer to the nearest cent.
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1200\\ r=rate\to 0.2\%\to \frac{0.2}{100}\dotfill &0.002\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{weekly, thus fifty two} \end{array}\dotfill &52\\ t=years\dotfill &10 \end{cases} \\\\\\ A = 1200\left(1+\frac{0.002}{52}\right)^{52\cdot 10}\implies A \approx 1224.24[/tex]
Answer: $1248 in compound interest for 10 years
Step-by-step explanation:
Now imagine the quadrilateral is the base of a prism that has a height of h
units. What is the volume of this prism compared to the one with a height of 1
unit? The volume of the prism is Bh, which is h times the volume
V of the
original prism.
right prism
The volume of the prism with height h is h times the volume of the prism with height 1 unit.
If the original prism has a volume of V and a height of 1 unit, then the volume of the prism with height h is given by:
Bh = (V)(h)
where B is the area of the quadrilateral base.
The volume of the prism with height h is h times the volume of the original prism. So, we can compare the volume of the two prisms by looking at their volume ratios:
Volume ratio = Volume of prism with height h / Volume of original prism
= Bh / (V)(1)
= Bh / V
= h
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Gary works at a bicycle store in Vancouver. For the start of spring, the manager of the store has ordered 50 mountain bikes and 10 racing bikes.
Which conjecture is Gary most likely to make from this evidence?
Answer and Step-by-step explanation:
Based on the evidence provided, Gary is most likely to make the conjecture that the store expects high demand for mountain bikes in the spring compared to racing bikes. Another conjecture that could be made is that mountain bikes will most likely sell better than racing bikes. This is because the manager has ordered 50 mountain bikes, which is five times more than the number of racing bikes ordered. This suggests that the store is anticipating greater demand for mountain bikes than for racing bikes in the spring season.
En un salón de clase de 60 alumnos, se tomaron 3 exámenes para aprobar un curso y se
observó que los que aprobaron un solo examen es el quíntuple de los que aprobaron los
3 exámenes y los que aprobaron sólo 2 exámenes es el triple de los que desaprobaron
los 3 exámenes. Si el número de los que desaprobaron los 3 exámenes es igual al número
de los que aprobaron los 3 exámenes, cuántos aprobaron el curso si para aprobarlo es
necesario que aprueben por lo menos 2 exámenes?
Translate: In a classroom of 60 students, 3 exams were taken to pass a course and
He noted that those who passed a single exam were five times those who passed the
3 exams and those who passed only 2 exams is triple those who failed
the 3 exams. If the number of those who failed the 3 exams is equal to the number
Of those who passed the 3 exams, how many passed the course if to pass it is
Do they need to pass at least 2 exams?
The number of students who passed the course is x + 3y, where x is smallest integer greater than or equal to[tex](180 - 3z)/53[/tex], and y = [tex](60 - 7x)/3[/tex] for equal things.
Let's use some variables to represent the number of students who passed each exam:
Let's call the number of students who passed all 3 exams "x".
Let's call the number of students who passed exactly 2 exams "3y" (since it's given that this number is triple the number who failed all 3 exams).
Let's call the number of students who passed exactly 1 exam "5x" (since it's given that this number is five times the number who passed all 3 exams).
Finally, let's call the number of students who failed all 3 exams "x".
We can use this information to set up a system of equations:
x + 3y + 5x + x = 60 (since there are 60 students in total)
x = x (since the number who failed all 3 exams is equal to itself)
Simplify:
7x + 3y = 60
Now we need to use the fact that passing at least 2 exams is required to pass the course. This means we need to find the number of students who passed at least 2 exams, which is the sum of the number who passed all 3 exams and the number who passed exactly 2 exams:
x + 3y
We know that this number needs to be greater than or equal to the number of students who pass the course. So we set up another equation:
x + 3y >= z (where z is the number of students who pass the course)
Now we can solve for x and y in terms of z. We'll start with y:
7x + 3y = 60
3y = 60 - 7x
y = (60 - 7x)/3
Next, we'll use the fact that the number who failed all 3 exams is equal to the number who passed all 3 exams:
x = x
Finally, we'll use this information to solve for x in terms of z:
x + 3y >= z
x + 3((60 - 7x)/3) >= z
x + (60 - 7x) >= 3z
53x >= 180 - 3z
x >= (180 - 3z)/53
Since x represents the number of students who passed all 3 exams, we want to round it up to the nearest integer (since we can't have a fractional number of students). So the final answer is:
The number of students who passed the course is x + 3y, where x is the smallest integer greater than or equal to (180 - 3z)/53, and y is given by y = (60 - 7x)/3.
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