The predicted number of principals in attendance at the conference can be 161
What is the ratio?A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.
Given that,
A recent conference had 850 people in attendance.
In one exhibit room of 60 people, there were 46 teachers and 14 principals.
The predicated number of principals = ?
The ratio of teachers to principals = 60/14
= 30/7
In the same ratio there will be total teachers and principals:
Suppose, the number of teachers = x
the number of principals = y
x + y = 850
x/y = 30/7
x = (30/7)y
(30/7)y + y = 850
37y = 850 x 7
y = 161 (approx)
Hence, the number of principals cab be 161
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Answer:
D
Step-by-step explanation:
There were about 198 principals in attendance. EZ
what is 7/8 of 16 times in half of 30?
The simplification of the given expression would be = 210
How to simplify the given expression above?A fraction is defined as the expression of part of a whole value in the form of a denominator and a numerator.
The above statement can be expressed above mathematically as follows:
= 7/8 × 16 × 1/2× 30
= 3360/16
= 210
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Help, please thank you, and have a wonderful day
Help!!! I can’t even find the answer for this question
Answer:
<1 and <2
Step-by-step explanation:
Adjacent means angles that are next to each other. This is not the only pair, but <1 and <2 are adjacent.
2/3 of the students in Mrs. Gracie’s class are boys . If there are 27 students in the class, how many of them are girls?
Answer:
9
Step-by-step explanation:
divide 27 by 3
It equals 9
9 x 2 = 18 boys
27-18= 9 girls
Say that a certain stadium for professional football has 70,000 seats. What is the shape of the
supply curve for tickets to football games at that stadium? Explain.
Answer: The shape of the supply curve for tickets to football games at the stadium with 70,000 seats is upward-sloping. This means that as the price of tickets increases, the quantity of tickets supplied also increases.
The reasoning behind this is simple: when the price of tickets is high, there is more incentive for the sellers (e.g. the stadium, ticket resellers, etc.) to sell more tickets. They have the ability to supply more tickets as the demand for tickets at the high price is likely to be higher, thus increasing their profits.
However, it is important to note that the upward slope of the supply curve is not necessarily linear. The supply curve for tickets to football games is likely to be more elastic in the higher price range, meaning that as the price continues to increase, the quantity supplied may increase at a slower rate. This is because at some point, even if the price continues to rise, there will be a limit to how many tickets can actually be sold due to a decrease in demand.
Overall, the upward-sloping shape of the supply curve for tickets to football games at the stadium with 70,000 seats reflects the basic principle of supply and demand: as the price increases, the quantity supplied will also increase, but at some point, the increase in price will lead to a decrease in demand, limiting the quantity supplied.
Step-by-step explanation:
Reactive Power VARS Apparent Power VA CD True Power W
a. Reactive power is the power lost in the inductive or capacitive load in an AC electrical circuit.
b. Apparent power is the power is the total power delivered to an AC electrical circuit
c. True power is the power lost in a resistive load in an AC electrical circuit.
What is power?Power is the rate at which work is done.
a. What is reactive power VARS?Reactive power is the power lost in the inductive or capacitive load in an AC electrical circuit. The reactive power is given by
P' = IVsinФ where
I = current in circuit, V = voltage in circuit and Ф = load angleb. What is apparent power VA?Apparent power is the power is the total power delivered to an AC electrical circuit. The apparent power is given by
S = IV where
I = current in circuit, V = voltage in circuit c. What is true power W?True power is the power lost in a resistive load in an AC electrical circuit. The true power is given by
P' = IVcosФ where
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Winnie made headbands to sell at the school craft fair. She sells each
headband for $6.25 and her goal is to earn at least $50.00. Write and solve
an inequality to represent this situation, where h represents the number
of headbands Winnie must sell in order to reach her goal.
Answer:
6.25 x h = 50.000
Step-by-step explanation:
Answer:
8 headbands.
Step-by-step explanation:
Winnie needs to sell AT LEAST 8 headbands. 50 divided by 6.25 is 8. Remember that the phrase "at least" is represented by a greater-than-or-equal-to symbol.
-(3x+1)+7=4-(3x + 2)
Show work
Answer:
no solution
Step-by-step explanation:
- (3x + 1) + 7 = 4 - (3x + 2) ← distribute parenthesis on both sides
- 3x - 3 + 7 = 4 - 3x - 2
- 3x + 4 = 2 - 3x ( subtract 4 from both sides )
- 3x = - 2 - 3x ( add 3x to both sides )
0 = - 2 ← false statement
this false statement indicates the equation has no solution
-(3x+1)+7=4-(3x + 2)
-3x-1+7=4-3x-2
-3x+6=-3x+2
-3x+3x=-4
0=-4
no solution
Claudia records the hours is been studying and a test scores for five test
The correlation coefficient when Claudia records the hours she spent studying and her test scores for 5 tests is 0.85. This is a strong positive correlation.
How to explain the correlationAny statistical association between two random variables or bivariate data, whether causal or not, is referred to as dependence or correlation.
Two variables that move together, or in the same direction, are said to have a positive correlation. When one variable rises while the other rises or when one variable falls while the other falls, there is a positive correlation. Theoretically, the same external forces can affect both of these separate variables because they travel in the same direction.
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Claudia records the hours she spent studying and her test scores for 5 tests.
What is the correlation coefficient?
-0.85-0.840.840.85
What is the strength of the model?
Put a decimal point in the number 26583 so that the 5 has a value of
100
50
The number as decimal is 26583.0
How to rewrite the number as decimalFrom the question, we have the following parameters that can be used in our computation:
Number = 26583
Also, we have the required value of 5 to be
Required = 100
Using the above as a guide, we have the following:
The number 5 must have a value of 100 in the new number i.e. 500
So, we have
Number = 26583
Rewrite as
Number = 26500 + 83
This means that we add 5 at the end
So, we have
Number = 26583.0
Hence, the new number is 26583.0
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For every 3 lemons you buy at a farm stand, the total cost increases by $1.80.
The constant of proportionality is
An equation that relates the total cost y and the number of lemons x is y=____x
Use the equation you wrote to complete the table.
Answer:
he constant of proportionality is $1.80, since for every 3 lemons the total cost increases by $1.80.
The equation that relates the total cost, y, and the number of lemons, x, is:
y = 1.80 * (x/3) + b
where b is the y-intercept, which represents the cost of 0 lemons. We'll need additional information to determine the value of b.
Here is a table with the values of y and x, assuming b = 0:
x (Number of Lemons) y (Total Cost)
0 0
3 1.80
6 3.60
9 5.40
... ...
Step-by-step explanation:
Two gliders collide on an air track. Glider 1 has a mass of 7. 0 kg, and glider 2 has a mass of 4. 0 kg. Before the collision, glider 1 had a velocity of 2. 0 m/s, and glider 2 had a velocity of -5. 0 m/s. If the collision is perfectly elastic, what is the total kinetic energy of both gliders after the collision?
A. -36. 0 J
B. 36. 0 J
C. 64. 0 J
D. 128. 0 J
For the information provided, the total kinetic energy of both gliders after collision is 13.5 J. In an elastic collision, both momentum and kinetic energy are conserved.
The momentum conservation principle states that the total momentum of the system before the collision is equal to the total momentum after the collision. Mathematically, we can write this as:
m₁v₁i + m₂v₂i = m₁v₁f + m₂v₂f
where m₁ and v₁i are the mass and initial velocity of glider 1, m₂ and v₂i are the mass and initial velocity of glider 2, and v₁f and v₂f are their velocities after the collision.
Using this equation and the given values, we can solve for the final velocities:
(7.0 kg)(2.0 m/s) + (4.0 kg)(-5.0 m/s) = (7.0 kg)v₁f + (4.0 kg)v₂f
14.0 kg·m/s - 20.0 kg·m/s = 7.0 kg·v₁f + 4.0 kg·v₂f
-6.0 kg·m/s = 7.0 kg·v₁f + 4.0 kg·v₂f ---(1)
The kinetic energy of an object is given by the equation:
KE = 1/2 mv²
Therefore, the total kinetic energy of both gliders after the collision can be calculated as:
KE_total = 1/2 m₁ v₁f² + 1/2 m₂ v₂f²
Substituting the values of m₁, m₂, v₁f, and v₂f from equation (1) into this equation, we get:
KE_total = 1/2 (7.0 kg) (0.86 m/s²) + 1/2 (4.0 kg) (5.14 m/s²)
KE_total = 13.5 J
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A population p of migrating butterflies satisfies the equation p = 100,000 -
100,000 (4/5)"
where w is the number of weeks since they began their migration.
Complete the table with the population after different numbers of weeks.
W
р
0
100000
1
20000
2
4000
What is the vertical intercept of the graph?
800
3
160
The vertical intercept of the graph is 100,000
What is an exponential function?A function whose value is a constant raised to the power of the argument, especially the function where the constant is e, is called an exponential function.
Given that, the population p of migrating butterflies satisfies the exponential function p = 100,000 (4/5)ⁿ, where n is the number of weeks,
So, we need to find the vertical intercept of the graph,
We know that, vertical intercept = intercept
To find the y-intercept of a line, we will put x = 0,
here x is n,
So, the y-intercept of the graph is = 100,000 (4/5)⁰ = 100,000×1 = 100,000
Therefore, the vertical intercept of the graph is 100,000
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Write the equation of the graph shown below in factored form
The equation of the polynomial is P(x) = -4(x + 1)(x - 1)(x - 2)^2
How to determine the equation of the polynomialFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the following readings:
A root of multiplicity 1 at x = -1A root of multiplicity 1 at x = 1A root of multiplicity 2 at x = 2y-intercept = -12A polynomial is represented as
P(x) = a * (x - zero)^multiplicity
Using the above as a guide, we have the following:
P(x) = a * (x + 1)(x - 1)(x - 2)^2
The y-intercept is -12
So, we have
a * (0 + 1)(0 - 1)(0 - 2)^2 = -12
This gives
a = -4
Hence, the expression is P(x) = -4(x + 1)(x - 1)(x - 2)^2
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100 points!!!!!!!!
Martina is playing a carnival game. She is blindfolded while she throws a dart at a board of 12 balloons, as shown below. Each balloon is labeled "S" for small,
"M" for medium, "L" for large, or "XL" for extra-large. The board has 5 small balloons, 1 medium balloon, 4 large balloons, and 2 extra-large balloons. She hits one of the balloons at random and wins a stuffed animal of that size.
(a)Find the odds in favor of Martina winning a medium stuffed animal.
(b) Find the odds against Martina winning a medium stuffed animal.
Answer:
(a) The odds in favor of Martina winning a medium stuffed animal is 1/12, as there is only 1 medium balloon on the board out of the total of 12 balloons.
(b) The odds against Martina winning a medium stuffed animal is 11/12, as there are 11 balloons on the board that are not medium out of the total of 12 balloons.
Answer:
(a) The odds in favor of Martina winning a medium stuffed animal is 1/12, as there is only 1 medium balloon on the board out of the total of 12 balloons.
(b) The odds against Martina winning a medium stuffed animal is 11/12, as there are 11 balloons on the board that are not medium out of the total of 12 balloons.
Solve the inequality √x+2 > -1.
The final inequality is x > - 1.
Option D is the correct answer.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
√(x + 2) > -1
Squaring both sides.
x + 2 > (-1)²
x + 2 > 1
Subtracting 2 on both sides.
x > 1 - 2
x > -1
Thus,
x > - 1 is the final inequality.
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help me find the measure
Answer:
= 60°
Step-by-step explanation:
Exterior angle =
[tex] = \frac{360}{n} [/tex]
[tex] = \frac{360}{6} \\ = {60}^{o} [/tex]
= 60°
Please helpppp!!!!!!
Step-by-step explanation:
On the region, (-oo,0.5), the graph formes a upside U shaped , this mean the graph is concave down on this region. this implies that our second derivative is negative and our first derivative is changing negatively.
The graph is concave up from (0.5,oo) since the graph formes a U shape.
This also implies that (0.5) is a inflection point
The function crosses the x axis at -1,0,3
So the 2nd,3rd,6th, 7th options are correct
For a particular 4 leaf clover, the highway had to be compacted on the south side making the circles two different sizes. The two circles on the north of the highway have a radius of 128 feet and the two on the south side have radius of 102 feetCalculate the total area of grass seed needed for these four circles
The total area of the two circles will be 168316.9 square feet.
What is a circle?The circle is defined as a two-dimensional figure having a fixed point and the number of the points is traced around the curved path at an equal distance from the fixed point. The overall figure is called a circle.
The area of the circle is calculated by the formula:-
Area = πr²
Given that the south side of the highway needed to be compacted in order to create two circles of various sizes for a specific four-leaf clover. The two circles on the north side of the road have a 128-foot radius, whereas the two on the south side have a 102-foot radius.
The total area will be calculated as:-
Area = 2 x π x 128² + 2 x π x 102²
Area = 102943.25 + 65370.25
Area = 168316.9 square feet
Hence, the total area will be 168316.9 square feet.
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An international company has 21,800 employees in one country. If this represents 32.2% of the company's employees, how many employees does it have in
total?
Round your answer to the nearest whole number.
employees
X
Español
?
D
Answer:
Step-by-step explanation:
The international company has 21,800 employees in one country, which represents 32.2% of the company's total employees. We can use this information to find the total number of employees by solving for the missing value.
Let's call the total number of employees in the company "X".
If the 21,800 employees in one country represent 32.2% of the total employees, we can write an equation to represent this relationship:
0.322 * X = 21,800
Next, we'll isolate X by dividing both sides of the equation by 0.322:
X = 21,800 / 0.322
Using a calculator, we can find that:
X = 68,062.5
Rounding to the nearest whole number, the company has 68,063 employees in total.
So, that's how you can use a percentage to find the total number of employees in the company. By knowing the number of employees in one country and the percentage that this represents of the total, we can find the total number of employees in the company.
See attached image and answer questions.
The properties of the polynomial are
Degree = oddLeading coefficient = NegativeOdd multiplicity = 3Even multiplicity = 1How to determine the properties of the polynomialFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the following readings:
A root of multiplicity 1 at x = -5A root of multiplicity 1 at x = -2A root of multiplicity 2 at x = 1A root of multiplicity 1 at x = 4y-intercept = 2Using the above as a guide, we have the following:
Degree = sum of multiplicities
Degree = 1 + 1 + 2 + 1
Degree = 5
The leading coefficient is negative
This is so because the graph opens down
There are 3 zeros with odd multiplicities and 1 zero with even multiplicity
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Select all of these coordinates that lie on the
line y = 1-2x.
(-5, -9) (-3,7) (4,9) (6, -11)
The coordinates that lie on the equation of line y = 1 - 2x are P ( -3 , 7 ) and Q ( 6, -11)
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( -3 , 7 )
Let the second point be Q ( 6 , -11 )
The equation of line is y = 1 - 2x
Substituting the values of x and y in the equation , we get
when x = -3
y = 1 - 2 ( -3 )
y = 1 + 6
y = 7
when x = 6
y = 1 - 2 ( 6 )
y = 1 - 12
y = -11
Hence , the coordinates of the equation of line are P ( -3 , 7 ) and Q ( 6, -11 )
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Claudia is interested in knowing which figure skater competing in the
Olympic Games is most favored to win a gold medal. To sample the
students in her school, she prepares a list of all of the boys and girls in the
school and randomly chooses a sample from each group so that the size of
each group is proportional to the number of boys and girls in the school.
Which sampling method did Claudia use?
OA) simple random sampling
OB) stratified random sampling
OC) systematic random sampling
OD) simple non-random sampling
OD) Is simple non-randon sampling
Step-by-step explanation:
because Claudia randomly choose a sample from each group.
Hasten plans to choose a book from the section of the store where everything is 25% off he likes expression D -0.25 days to find the sale price of the book it if there is a YZ dollars below correctly write another expression 0.7 5D that will also find the surprise of the book if the original price is de dollars
Another form of representing the cost of the book is (75/100)×D.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
We know, Percentages and decimals are related.
10% in decimal form is equivalent to (10/100) - 0.1 in decimal.
An expression that represents the sale day book price is 0.75D.
Another expression that would represent the cost of the book priced 'D' would be,
= (75/100)×D.
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Choose all of the values that are solutions to inequality x < -2
Answer:
The solution to the inequality x < -2 is all real numbers that are less than -2. This means that any number that is less than -2 will satisfy the inequality, but any number that is greater than or equal to -2 will not.
So, the solution set for x < -2 is all real numbers that are less than -2. This solution set can be expressed as (-∞, -2).
Therefore, the values that are solutions to the inequality x < -2 are:
• all real numbers less than -2, such as -3, -4, -5, etc.
Note that -2 itself is not part of the solution set, since it is not less than -2.
The average mass of a certain type of microorganism is 2.4×10^ −6
grams. What is the approximate total mass of 5,000 of these microorganisms?
0.0012 g
0.012
0.12 g
0.00012 g
Answer:
Below
Step-by-step explanation:
5000 * 2.4 x 10^-6 =
12 000 x 10^-6 g
= .012 g
In simple terms, please explain to me what is the difference between horizontal shrink and vertical stretch.
Answer:
see attached
Step-by-step explanation:
You want the difference between horizontal shrink and vertical stretch.
Horizontal shrinkA horizontal shrink compresses a graph horizontally. In the attached figure, the original graph is the red circle. The blue ellipse is that circle shrunk horizontally by a factor of 3. It retains the same height, but is compressed sideways.
Vertical stretchA vertical stretch expands the graph vertically. The green ellipse in the attached figure is the original circle stretched vertically by a factor of 3. The horizontal dimension remains unchanged.
InterchangeableYou will notice that replacing a variable x by x/k effectively accomplishes a stretch by a factor of k in that variable's direction. Similarly, replacing a variable x by kx accomplishes a compression by a factor of k.
Your question suggests that you have noticed the similarities between vertical stretch and horizontal compression. For some figures, there is basically no difference.
Here are a couple of examples of that:
line y = x. Vertical stretch by 2: y/2 = x, or y = 2x. Horizontal compression by 2: y = 2x. These equations are identical.
parabola y = x². Vertical stretch by 4: y/4 = x² or y = 4x². Horizontal compression by 2: y = (2x)² = 4x². These equations are identical.
DifferencesThe differences between stretch in one direction and compression in the other direction are more apparent for figures with multiple reversals of direction. The second attachment shows the sine function (red) vertically stretched (blue) and horizontally compressed (green).
create a table of values to represent the total cost if ben orders 1 or 2 books or spends 41$, $65 OR $125
The table to represents the total cost for the different numbers of books ordered is:
Number of books Spending Total cost
1 $41 $44
2 $65 $71
3 $125 $134
What is an expression?An expression is written with one or more terms with addition, subtraction, multiplication, and division.
Example:
2.2 + 3x + 4y = 7 is an expression.
3 + 5x = 9 is an expression.
We have,
The book cost = $3
Now,
Spendings = $41, $65, or $125
Now,
Table:
Number of books Spending Total cost
1 $41 41 + 3 = $44
2 $65 65 + 6 = $71
3 $125 125 + 9 = $134
Thus,
The table for the total cost is given above.
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A business puchases a computer system for $3,000. The value of the system decreases at a rate of 15% per year. Write an exponentioal function to model this situation. Then determine how much the comoputer will be work after 3 years
Value of system after 'x' years = [tex]3000*(0.85)^x[/tex]
The value of the computer after 3 years is $1842.375
What is an exponential function?The formula for an exponential function is f(x) =[tex]a^x[/tex], where 'x' is variable and 'a' is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.
Given that, computer system values at $3000 decrease at a rate of 15% each year.
If the value decreases by 15%, it means that the new value is 85% of the old value.
new value = old value * (85/100)
new value = old value * 0.85
value in 1st year = $3000
value after 1st year = $3000 * 0.85
value after 2nd year = $3000 * 0.85 * 0.85
value after nth year = $3000 * [tex]0.85^n[/tex]
Value of the system after 3 years = $3000 * [tex]0.85^3[/tex]
= $3000 * 0.614125
= $1842.375
Therefore, The value of the computer system after 3 years is $1842.375
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A picture of a family crest is 5.1 inches wide. The family needs a reduced copy for the front page of the family
newsletter. The copy must fit in a space 1.3 inches wide. What scale factor should be used on the copy machine to
adjust the size of the picture of the crest?
Answer:
0.255 or 25.5%
Step-by-step explanation:
You want the scale factor that reduces 5.1 inches to 1.3 inches.
Scale factorThe scale factor is the ratio of the image size to the original size:
1.3/5.1 ≈ 0.254902 ≈ 0.255 = 25.5%
__
Additional comment
A scale factor of 0.255 would give an image of 1.3005 inches. That's probably close enough. Rounding to the nearest percent, it would be 25%, which would give an image size of 1.275 inches.
