Answer:
In 2005, there were 1,200 students at the school.
Step-by-step explanation:
In 2005, there were 1,200 students at the school. This can be calculated by taking 85% of 1020 (the number of students in 2006) and multiplying it by 100. 85% of 1020 is 861. Multiplying this by 100 gives us 86,100. Dividing this by 85 gives us 1,200. Therefore, in 2005 there were 1,200 students at the school.
How many quarts are in 4 gallons?
Answer:
4 US liquid gallons = 16 US liquid quarts
( Multiply the volume value by 4 )
Have a wonderful day! :-)
Answer:
16 quarts in 4 gallons
Step-by-step explanation:
1 gallon equals 4 quarts
How do you prove the isosceles triangle theorem?
To prove the isosceles triangle theorem, you must use the fact that the base angles of an equilateral triangle have equal measure, and then use the properties of isosceles triangles to show that the two angles opposite the equal sides are also equal.
To prove the isosceles triangle theorem, we can follow these steps:
Step 1: Draw an isosceles triangle with sides AB and AC of equal length.
Step 2: Draw a line from point A to point D, perpendicular to line BC.
Step 3: Use the definition of an isosceles triangle to state that ∠ABD and ∠ACD are congruent.
Step 4: Use the definition of a perpendicular line to state that ∠ADB and ∠ADC are congruent.
Step 5: Use the definition of a triangle to state that ∠BAC and ∠BAC are congruent.
Step 6: Use the Congruent Triangles Postulate to state that triangle ABD and triangle ACD are congruent.
Step 7: Use the definition of congruent triangles to state that ∠ABC and ∠ACB are congruent.
Step 8: Use the definition of an isosceles triangle to conclude that the isosceles triangle theorem is true.
Therefore, we have proven the isosceles triangle theorem, which states that the base angles of an isosceles triangle are congruent.
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How do you convert microl to l?
Microliters (µL) and liters (L) are both units of volume measurement. A microliter is a very small unit of volume, equivalent to one millionth of a liter. To convert microliters to liters, we can use a simple conversion factor.
The conversion factor is based on the fact that one liter is equivalent to one million microliters. Therefore, to convert microliters to liters, we divide the number of microliters by one million. This can be expressed as:
L = µL / 1,000,000
For example, if we have a volume of 500 µL that we want to convert to liters, we can use the formula above as follows:
L = 500 µL / 1,000,000
L = 0.0005 L
Therefore, 500 µL is equivalent to 0.0005 liters.
It is important to keep track of the units when making conversions and to use appropriate significant figures. Additionally, it is worth noting that microliters are often used in situations where very small volumes are involved, such as in medical or laboratory settings, whereas liters are used for larger volumes such as in the context of cooking or liquid measurements.
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Please I nee help....
The area of the figure is 39 feet square.
How to find the area of a composite figure?A composite figure contains two or more shapes. The figure above is a composite figure. The area of the figure can be calculated as follows:
area of the figure = area of rectangle 1 + area of rectangle 2
Therefore,
area of rectangle 1 = lw
where
l = lengthw = widthTherefore,
area of rectangle 1 = 2(3)
area of rectangle 1 = 6 ft²
area of rectangle 2 = 11 × 3
area of rectangle 2 = 33 ft²
Therefore,
area of the figure = 6 + 33
area of the figure = 39 ft²
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DUE TODAY HELP ASAP!!
The measure of {x} for each case is -
{ 1 } : x = 45
{ 2 } : x = 54.5
What is a parallelogram?In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.Given is a quadrilateral and a pentagon.
{ 1 } -
We can write -
2x + 3x + x + 90 = 360
6x + 90 = 360
6x = 270
x = 45 ... { 1 }
{ 2 } -
We can write -
5(2x - 1) = 540
2x - 1 = 108
2x = 109
x = 54.5 ... { 2 }
Therefore, the measure of {x} for each case is -
{ 1 } : x = 45
{ 2 } : x = 54.5
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Answer the statistical measures and create a box and whiskers plot for the following set of data. 4 , 6 , 7 , 7 , 7 , 9 , 9 , 12 , 13 , 13 , 14 , 14 4,6,7,7,7,9,9,12,13,13,14,14
Minimum value = 3 , Q₁ = 7.5 , Median = 10 , Q₃ = 13 and maximum value = 16 of the given data set.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
According to the question,
Minimum value of the given data set = 3
n = number of data set
First arrange the data in ascending order
3,4,6,7,8,9,10,10,12,12,13,13,15,16
Quartiles
Q₁ = [ (n+1)/4]th term
= 14 +1 / 4
= 3.75th term
= 3th term + 0.75 ( 4th term - 3th term)
= 6 + 0.75 (7 -6)
= 6.75
As n is even,
Median = (N/2)th term
= 14 /2
= 7th term
= 10
Q₃ = [3(n+1)/4]th term
= 3 × 3.75
= 11.25
= 11th term +0.25( 12th term - 11th term)
= 13 + 0.25 (13 -13)
= 13
Maximum value = 16
Hence, Minimum value = 3 , Q₁ = 7.5 , Median = 10 , Q₃ = 13 and maximum value = 16 of the given data set.
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The complete question in attachment
A survey of all beings on planet Quect found that 30% preferred
pisquet juice to all other juices. If 6 beings preferred pisquet juice,
how many beings were surveyed altogether?
The total number of beings surveyed is given by the equation A = 20
What is Percentage?A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.
Percentage change is the difference between the measured value and the true value , as a percentage of the true value
Percentage change =( (| Measured Value - True Value |) / True Value ) x 100
Given data ,
Let the total number of beings surveyed be represented as A
Now , the percentage of beings preferred pisquet juice = 30 %
The number of beings who preferred pisquet juice = 6
Substituting the values in the equation , we get
( 30 ) % of A = 6 be equation (1)
On simplifying the equation , we get
( 30/100 )A = 6
Multiply by 100 on both sides of the equation , we get
30A = 600
Divide by 30 on both sides of the equation , we get
A = 600/30
A = 20
Therefore , the value of A is 20
Hence , the number of beings is 20
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HELP ASAP
The table shows values for Variable A and Variable B.
Variable A 1 5 2 7 8 1 3 7 6 6 2 9 7 5 2
Variable B
3 5 4 7 7 4 4 6 6 13 3 8 8 6 1
Use the data from the table to create a scatter plot.
Keyboard Instructions
Initial graph state
The horizontal axis goes from -0.7 to 10.5 with ticks spaced every 1 unit(s).
The vertical axis goes from -1 to 14.5 with ticks spaced every 1 unit(s).
The value of x is 77.5. The Triangle Angle Sum Theorem states that the sum of the angles in a triangle is 180°.
What is value?Value is a subjective concept that referred to the word of importance that an individual group of people places on something it is often associated with principal beliefs and standard that are accepted by society when you can be seen as a measure of how important something is true person of organization it is often seen as a reflection of ones worldview and can help to save attitudes decision and behaviors believe is not an absolute and very depending on the context of the looks like commands.
In order to solve for x, we need to use the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle is 180°. Since angle BAC is bisected by segment AD, the two angles must be equal. Therefore, we can set up the following equation to solve for x:
180° = angle BAC = (x + 7) + (x + 18)
We can solve this equation by combining like terms and isolating the variable x.
180° = 2x + 25
2x = 155
x = 77.5
Therefore, the value of x is 77.5.
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what is 10 mcg to mg ?
Using the conversion from microgram to milligram, we get, 10mcg is equal to 0.01mg.
1 mcg (microgram) is equal to 0.001 mg (milligrams). Therefore, to convert 10mcg to mg, we simply need to multiply 10 by 0.001:
10 mcg * 0.001 mg/mcg = 0.01 mg
So, 10mcg is equal to 0.01mg.
To explain further, the prefix "micro" means one millionth (1/1,000,000), while the prefix "milli" means one thousandth (1/1,000). Therefore, to convert a value from micrograms to milligrams, we need to divide the value by 1000 (or multiply by 0.001), because there are 1000 micrograms in a milligram. It is important to use the correct units when working with medication dosages, as small differences in dose can have significant effects on the patient's health.
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my question is in the screenshot
The initial amount of stickers given to each of the volunteers was 4 stickers while the final amount given to each of them was 6 stickers.
How to solve Algebra Word problems?We are told that Mai gave each of the five volunteers the same number of stickers. Thereafter, she gave each of them 2 stickers each and the total was 30 stickers.
If the initial amount given to them each was y, then we have;
5(y + 2) = 30
y + 2 = 6
y = 6 - 2
y = 4
Thus, we can say that the amount of stickers she gave each of them initially was 4 stickers while the amount she gave them in total after the extra ones was 6 each
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This one dont make sense
Answer: x=6
Step-by-step explanation:
90-75=15
15-3=12
12/2=6
the little box means 90 degree angle
Answer:
x = 6
Step-by-step explanation:
Complementary angles:
If sum of two angles add up to 90°, they are called complementary angles.
75 + 2x +3 = 90
2x + 78 = 90
Subtract 78 from both sides,
2x = 90 - 78
2x = 12
Divide both sides by 2
x = 12÷2
x = 6°
2x + 3 = 2*6 + 3
= 12 + 3
= 15°
S
ir br
5. A company is designing a new
cylindrical package. The volume of
the package is 87.92 in.³. The
radius is 2 inches. Use 3.14 to
approximate 7 to answer the
questions.
Part A
To the nearest inch, how many
inches is the height of the
cylindrical package?
Answer:
Step-by-step explanation:
87.92*3.14/4=504.3
A bag contains pennies, nickels, dimes, and quarters. There are 50 coins in all. Of the coins, 14% are pennies and 40% are dimes. There are 6 more nickels than pennies. How much money does the bag contain?
The bag that contains pennies, nickels, dimes, and quarters have the total amount of 5.26 dollars.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
A bag contains 50 coins
Now, Number of pennies = 14% of 50
= 0.14 × 50
= 7 pennies
and, Number of dimes = 40% of 50
= 0.40 × 50
= 20 dimes
Number of nickels = 6 more than pennies
= 6 + 7
= 13 nickles
Number of quarters = Rest of the coins
= 50 - (7 + 20 + 13)
= 50 - 40
= 10 quarters
As we know,
1 penny = 0.01 dollar
7 pennies = 0.01 ×7 = 0.07 dollar
1 dime = 0.10 dollar
20 dimes = 0.10 × 20 = 2.00 dollar
1 nickel = 0.05 dollar
13 nickel = 0.05 × 13 = 0.65 dollar
1 quarter = 0.25 dollar
10 quarter = 0.25 × 10 = 2.50 dollars
Total value of the coins in the bag = 0.07 + 2.00 + 0.65 + 2.50
= 5.22 dollars
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cesar had $60.he spent $36.90 on a pair of shoes and the rest new shirt
a)what percent of his money did he spend on the shoes
b)what percent of the hair clips were purple
Answer:
(a) 61.5%
Step-by-step explanation:
(a) $36.90/$60*100%= 61.5%
Write an equation in slope-intercept form for the line that passes through (8,1) and (4,3).
A. y= 1/2x + 5
B. y= −2x + 5
C. y= −1/2x + 5
D. y= −1/2x + 15
Answer:
The answer would be part C
Step-by-step explanation:
First we find the gradient by y2-y1/x2-x1
So it would be;
3-1/4-8
2/-4
-1/2
Now we put in the gradient and the points (4,3) in the equation y=mx+c;
3=-1/2(4)+c
3=-2+c
3+2=c
5=c
Finally we put c in the equation;
y=mx+c
y=-1/2x + 5
What is the value of x?
The value of x is 2√13 units.
The correct option is D.
What is Pythagoras' theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.
Given:
A right-angled triangle.
The value of the base is 12 units.
And the length of the perpendicular is 8 units.
Therefore,
x = √{(8)² + (12)²}
x = √(64 + 144)
x = √208
x = 2√13
Therefore, x = 2√13.
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Im really stuck on this
The triangular area abc, from the graph on the market for gasoline represents, D. the deadweight loss (or excess burden) created by the tax.
What is a deadweight loss ?The cost of market inefficiency, which happens when supply and demand are out of balance, is known as a deadweight loss. When supply and demand are out of equilibrium, a deadweight loss arises, which impairs the efficiency of the market.
Deadweight losses may result from price floors, such as minimum wage and living wage regulations, price ceilings like price controls and rent restrictions, and taxation. A society's resource distribution may also become inefficient with a decline in commerce.
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The variables X and Y have a proportional relationship and Y equals 2/5 when X equals 5/8 which Quetion represents this relationship
A. Y= 1 9/16x
B. Y= 16/25x
C. Y= 9/40x
D. Y=1/4x
What is the value of this expression when c=-4 d= 10
Answer:
9
Step-by-step explanation:
If c = -4 d = 10, we can re-write the expression:
[tex]\frac{1}{4} (-4^{3}+10^{2} )[/tex]Simplifying what is in the parenthesis:
[tex]\frac{1}{4} (-64 +100)[/tex][tex]\frac{1}{4}[/tex] × 369Therefore when c = -4 d = 10, [tex]\frac{1}{4} (-4^{3}+10^{2} ) = 9[/tex].
Answer: B. 9
Step-by-step explanation:
Let's learn some BIDMAS rules!
BIDMAS is an order of operation.
Multiply first or the indices? We can solve it with order of operations.
Here we go ↓↓
B = Brackets
I = Indices (³ ²)
D = Division
M = Multiplication
A = Addition
S = Subtraction
NOTE = Multiply or divide first? We do it from left to right
NOTE = Addition or Subtraction? We also do it from left to write in an equation.
Step 1 :
We replace all the letters with the given value, this make it :
[tex]1/4 (-4^{3} + 10^{2} )[/tex]=?
Step 2 :
Now, according to the rules, we do the numbers in the brackets first, now, in the brackets, there are indices, so we do those.
Which makes it :
1/4(-64+100)= ?
Step 3 :
Now we add the integers inside the brackets, remember, whenever the equation is like this, it is telling us it is a multiplication, here, it will be 1/4 x (-64+100) . In algebra, we don't use the × sign as it can be misinterpreted as [tex]x[/tex] .
1/4 (-64+100 = 36)
1/4 (36)
=
1/4 x 36
So we have = 1/4 x 36 at last.
Step 4 =
Do the multiplication!
1/4 x 36 = 9
So the answer is 9
Is it possible to sketch a graph of a quadratic polynomial function that has no turning points? Explain.
Particular attention should be paid to the y=x3+x graph, which lacks any stationary points of inflexion or turning points. This illustration demonstrates that a cubic graph could contain zero stationary points. One, two, or three x-intercepts can be found on the graph of a cubic polynomial.
What is meant by polynomial?A degree three polynomial might be referred to as a cubic polynomial. In other words, the number three will be the largest exponent of the variable in a cubic polynomial. A cubic polynomial would therefore have the generic form ax3+bx2+cx+d, where a0.Cubic polynomials have variables with highest exponents of three (3) or greater. Consequently, a polynomial of degree three is called a cubic polynomial. Degree 0 is known as the constant, degree 1 as linear, degree 2 as quadratic, degree 3 as cubic, degree 4 as quartic or the fourth degree, degree 5 as quintic or the fifth degree, and so forth.To learn more about polynomial, refer to:
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Coach Trevor packs a bag with 16 basketballs and footballs. The rato of basketballs to footballs is 5 : 3. Basketballs weigh 22 ounces, and footballs weigh 16 ounces, How much does the basketballs and footballs weigh in all?
Answer: 316 ounces
Step-by-step explanation:
5 + 3 = 8 (This tells us that there are a total of 8 "parts" in the ratio)
16/8 = 2 (Each part has a total of 2 balls)
2*5 = 10 basketballs
2*3 = 6 footballs
10 basketballs * 22 ounces = 220 ounces
6 footballs * 16 ounces = 96 ounces
Total = 220 + 96 = 316 ounces
Hoped this helped! Leave a comment if you have any other questions.
Which of the following gives the correct range for the graph?
5.01 Identifying functions.
A x:33333 Y:-2,-1,0,2,2
B: x:-3,-1,0,0,2 Y:3,3,3,-3,3
C: x: -4,-3,-2,1,1 Y: -3,1,-4,1,-2
D x:-2,-1,0,2,5 Y: 0,2,1,0,2
Answer: This question is asking for the range of the graph, which is the set of all possible values of the dependent variable (y-coordinate) in the graph.
Based on the options given, the correct range is:
D x:-2,-1,0,2,5 Y: 0,2,1,0,2
The range of this graph is {0, 1, 2}.
Step-by-step explanation:
Julian and Nikhil are making paper cones to hold popcorn to hand out at parent math night. They want the cones to hold 28.26 (about 9radius) cubic inches of popcorn. What are two different possible values for height h and radius r for the cones?
The two different possible values for height h and radius r for the cone is given by r = 2 inches , h = 6.746 inches
What is a Cone?A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the center of base) called the apex or vertex.
The volume of a cone is given by the equation
Volume of Cone = ( 1/3 ) πr²h
where r is the radius of the cone
h is the height of the cone
Surface area of the cone = πrl
where l = √ ( b² + r² )
Given data ,
Let the volume of the cone be represented as V
Now , the value of V = 28.26 inches³
Let the radius of the cone be r
Let the height of the cone be h
Volume of Cone = ( 1/3 ) πr²h
Substituting the values in the equation , we get
28.26 = ( 1/3 ) π ( r )² h
Multiply by 3 on both sides of the equation , we get
84.78 / π = r²h
26.986 = r²h
Now , when r = 2 inches
h = 26.986 / 4
h = 6.746 inches
And , when r = 3 inches
h = 26.986 / 9
h = 2.998 inches
Hence , the two values of radius and height of cone are solved
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Which of the following sentences describes the next step in the construction?
The sentence that describes the next step in the construction is; D: draw a line through points C and D
How to bisect a line?The steps that are used to bisect a line segment are;
1) Place the compass at one end of line segment.
2) Adjust the compass to slightly longer than half the line segment length
3) Draw arcs above and below the line.
4) Keeping the same compass width, draw arcs from other end of line.
5) Place ruler where the arcs cross, and draw the line segment.
From the given procedure and looking at the image, we can say that the next logical step would be to draw a line through points C and D
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Gwen has a home-based business making and selling scented soaps. She intially spent $96 to purchase soap-making equipment, and the materials for each kilogram of soap cost $9. Gwen sells the soap for $25 per kilogram. Eventually, she will sell enough soap to cover the cost of the equipment. How much soap will that be? What will be Gwen's total sales and costs be?
Gwen's total sales and costs would be; 50 dollars.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Consider that x represent the number of pounds of soap that she makes and eventually sells.
we are given that Gwen intially spent $96 to purchase soap-making equipment, and the materials for each pound of soap cost $9. This means that the total cost of making x pounds of soap would be;
9x + 96
thus her revenue for x pounds of soap would be
25 × x = 25x
If she eventually sells enough soap to cover the cost of the equipment, then we get;
9x + 96 = 25x
25x - 9x = 96
x = 96/16
x = 6
she would need to sell make and sell 6 soaps.
The cost would be 9x + 96 = 150
The total sales would be;
25 x 6 = 150
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Which of the following sentences describes the next step in the construction?
The sentence that best describes the next step in the construction of a square inscribed in a circle include the following: D. draw a line through points C and D.
What is a line segment?In Mathematics, a line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points. Additionally, a line segment typically has a fixed length.
In this scenario, the first step in the construction of a square inscribed in a circle is to draw line segment AB and then place your compass needle on any of the endpoints of line segment AB with arcs above and below, named line segment CD.
Furthermore, you should draw a straight line through point C and point D, wherein, line segment CD represent the perpendicular bisector of line segment AB.
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In the diagram O is the center of the circle if MABC equals 70 what is MAOC 
The measure of ∠AOC of the circle is ∠AOC = 140°
What is Central Angle?The central angle is an angle with two arms and a vertex in the middle of a circle. The two arms of the circle's two radii intersect the circle's arc at two separate locations. It is an angle whose vertex is the center of a circle with the two radii lines as its arms, that intersect at two different points on the circle.
The central angle of a circle formula is as follows.
Central Angle = ( s x 360° ) / 2πr
where s is the length of the arc
r is the radius of the circle
Central Angle = 2 x Angle in other segment
Given data ,
Let the measure of ∠ABC of the circle = 70°
Now , the sides AO and BO are the radius of the circle
where x + y = 70°
So , the measure of ∠AOB = 180 - 2x
And , the measure of ∠COB = 180 - 2y
Now , the measure of ∠AOC = 2 ( x + y )
On simplifying , we get
Central Angle = 2 x Angle in other segment
The measure of angle ∠AOC of the circle is = 2 ( 70 )°
The measure of angle ∠AOC of the circle is = 140°
Hence , the measure of ∠AOC of circle = 140°
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The change in the total amount of Suki's allowance balance over the course of four weeks is shown in the table.
Week Change ($)
1 25.25
2 ─5.75
3 12.40
4 ─14.35
Based on the average change in her allowance balance per week, how much money can Suki expect to save or spend over the course of a year?
Answer:
To get the average you add all numbers up then divide by the amount of numbers you have. In case it's 4 then you get your average dollar amount then you can calculate the amount for the years by multiplying it by 52 because there is 52 weeks in a year.
determine if the two triangles are congruent
Yes, the given pair of triangles are congruent by ASA rule.
What are congruent triangles?In geometry, two triangles are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
Given are two triangles, labelling by names, (refer to the image attached)
Considering the triangles, Δ ABC and Δ DEC,
We have,
AC = DC [given]
∠ A = ∠ D [both are congruent]
∠ ACB = ∠ DCE [vertically opposite angles]
∴ Δ ABC ≅ Δ DEC
By ASA rule.
Hence, we can say, the given pair of triangles are congruent by ASA rule.
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simplify 3a(6a^2-4ab^2)+8a^2b^2-2b^3
help? please and thank you
The simplified expression for this problem is given as follows:
18a³ - 4a²b² - 2b³.
How to simplify the expression?The expression for this problem is defined as follows:
3a(6a² - 4ab²) + 8a²b² - 2b³.
Applying the distributive property to the term 3a(6a² - 4ab²) , we have that:
3a(6a² - 4ab²) = 18a³ - 12a²b².
Hence the expression can be written as follows:
18a³ - 12a²b² + 8a²b² - 2b³.
-12a²b² + 8a²b² are like terms, hence:
-12a²b² + 8a²b² = -4a²b².
Meaning that the simplified expression is given as follows:
18a³ - 4a²b² - 2b³.
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