There are 15 two-point questions and 5 four-point questions.
What is an expression?
Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Let x be two-point questions and y be four-point questions. We know that there are 20 questions so the number of two-point questions plus the number of four-point questions equals 20. So x + y = 20. We also know that the total number of points is 50, so 2x + 4y = 50.
Solving the system:
1) x + y = 20
2) 2x + 4y = 50
Isolate x in 1) to get x = 20-y, then plug into 2)
2(20-y) + 4y = 50
2y=10
y = 5,
It means that there are 5 four-point questions. Plug y = 5 into either equation to get x = 15 so there are 15 two-point questions.
x + y = 20
x + 5 = 20
x = 15
Hence, there are 15 two-point questions and 5 four-point questions.
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Answer:
Step-by-step explanation:
the test ha 65 questions worth points and 5 questions worth 4 points
1 cup equals 16 tablespoons. how many tablespoons would be 1/4 cup of sugar
Answer:4 tablespoons
Step-by-step explanation:
1 = 16 tablespoons
1/4 = 4 tablespoons
Take 16 divided by 4 = 4
Point m is located at (5,-1) on the coordinate plane. Point M is reflected over the y axis to create point M. What ordered pair describes the location of M
The ordered pair that describes the location of M' is (-5, -1)
How to determine the ordered pair that describes the location of M?From the question, we have the following parameters that can be used in our computation:
Point M = (5, -1)
This point can be represented as
(x, y) = (5, -1)
Also, from the question, we have the transformation to be:
Point M is reflected over the y axis
Mathematically, this can be expressed as
(x, y) = (-x, y)
So, we have
Point M' = (-5, -1)
Hence, the image is (-5, -1)
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What is the answer to this problem?
Answer:
450x-9000
Step-by-step explanation:
You will be 9,000 dollars in debt, and it costs 300 dollars to make but sells for 750.
750-300 = 450 (profit per desk)
(0.25) to the power of 7 ⋅ 4 to the power of 7
The formula for 7 to the power of 4 is 74 = 7 7 7 7 = 2401.
What is the power of 7 to 4?The formula for 7 to the power of 4 is 74 = 7 7 7 7 = 2401.
To do this, you must multiply both the ordinates and the powers of ten portions of the two numbers (the mantissas).
In mathematics and algebra, multiplying seven occurrences of a given number by themselves yields the number's seventh power.
Consequently, n7 = n n n n n n.
Let's write 7 to the power of 4.0.2 to the power of 4 is 0.0016 one step at a time.
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NUMBER 4 PLEASE THIS IS URGENT
Answer:
its 5
Step-by-step explanation:
~Describe each transformation in words.
12.) _______________________.
The required transformations would carry reflection over the y-axis of the triangle in the given figure.
What is a transformation?A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.
The figure is given in the question,
According to the given graph, the required transformations would be as:
In the above illustration, the needed transformations would convey reflection over the y-axis of the triangle.
Thus, the required transformations would carry reflection over the y-axis of the triangle in the given figure.
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Neeeeeeeeed help please please
Answer:
Step-by-step explanation:
A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h (t) = 104t-16t^2. After how long will it reach its maximum height?
liters/minute, where t is in minutes since the pump is started. if the holding tank contains 1000 liters of water when the pump is started, approximately how much water does it hold two hours later?
Approximately, water does it hold two hours later is = 248.72 liters
Given that,
The holding tank contains 1000 liters of water
Water does it hold two hours later,
Then,
1) Integrate the function, from t =0 to t = 120 minutes to obtain the number of liters pumped out in the entire interval, and
2) Substract the result from the initial content of the tank (1000 liters).
So
We can write,
Let us assume,
Integral of (6 - 6 [tex]e^{-0.13t}[/tex] ) dt ]from t =0 to t = 120 min
= 6t + 6 [tex]e^{-0.13t}[/tex] / 0.13
= 6t + 46.1538 6 [tex]e^{-0.13t}[/tex] ] from t =0 to t = 120 min
= 6*120 + 46.1538 e^(-0.13*120) - 0 - 46.1538
= 720 + 46.1538 (1.678) - 46.1538
= 720 + 77.44 - 46.1538 liters
= 751.28 liters
2) If the holding tank contains 1000 liters of water,
1000 liters - 751.28 liters = 248.72 liters
Therefore,
Approximately, water does it hold two hours later is = 248.72 liters
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What is the value of x in the equation
8(x - 3) - 4x = 20?
A
x=−11
B
x=11
C
x=1
D
x=−1
Answer:
x = 11
Step-by-step explanation:
8(x-3) - 4x = 20
8x - 24 - 4x = 20
4x = 44
x = 11
Answer:
x=11
Step-by-step explanation:
8(x-3)-4x=20
8(x)+8(-3)-4x=20
8x-24-4x=20
4x-24=20
+24. +24
4x=44
/x. /x
x=11
Hopes this helps
Can someone pls simplify 2x-1/x^2 -2x-3 + 1/x-3
The simplified form of (2x - 1)/(x² - 2x - 3 + 1)/(x - 3) is
(2x - 1)(x - 3)/(x - 1 - √3)(x - 1 + √3).
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Given, (2x - 1)/(x² - 2x - 3 + 1)/(x - 3).
= (2x - 1)/(x² - 2x - 2)/(x - 3).
= (2x - 1)/(x - 1 - √3)(x - 1 + √3)/(x - 3).
= (2x - 1)(x - 3)/(x - 1 - √3)(x - 1 + √3).
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If a segment is drawn perpendicular to a line, the point of intersection is called the ____ of the perpendicular.
Answer: Foot
Step-by-step explanation:
The point of intersection is called the foot of the perpendicular. I remember learning this in my Math class!
Given the table below, write a linear equation that defines the dependent variable, p, in terms of the independent variable, t.
t
p
0
4
1
7
2
10
3
13
Show your work here
Enter your answer
Given the table below, write a linear equation that defines the dependent variable, p, in terms of the independent variable, t.
t. P
0. 4
1 7
2 10
3 13
Show your work here
Enter your answer
The required linear equation that defines the dependent variable, p, in terms of the independent variable, t is p = 3t + 4.
Explain linear equation?A linear equation is a mathematical condition of the structure y=mx+b. including just a steady and a first-request (straight) term, where m is the slant and b is the y-catch. Sometimes, the above is known as a "straight condition of two factors," where y and x are the factors.
According to question:Let linear equation be p = at + b
Where a and b are constant.
On putting the values from the table,
4 = 0×a + b
b = 4
and,
7 = 1×a + b ⇒ a + b = 7
a + 4 = 7
a = 3
Then,
p = 3t + 4
Thus, required equation is p = 3t + 4.
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Decide whether enough information is given to prove that the triangles are congruent using the HL Congruence Theorem. Explain.
Answer:
No
Step-by-step explanation:
You want to know if there is enough information to claim ∆PQT ≅ ∆SRT by the HL theorem.
HL theoremThe HL theorem tells you right triangles are congruent if they have one leg (L) and the hypotenuse (H) congruent.
Here, the triangles are not indicated as being right triangles, so the HL theorem cannot be applied.
__
Additional comment
There is not enough information here to permit the triangles to be declared congruent.
For congruence by any theorem, we'd need to know that angle T is the largest angle in each triangle, a condition not supported by the evidence.
Though rarely (if ever) seen in congruence discussions, a claim of SSA congruence can only be supported if the angle (A) is opposite the longest side. When the angle is 90°, this is called the HL congruence theorem. When the angle is known to be obtuse, it will always be opposite the longest side.
When the given angle is opposite the shortest of the two given sides, there are two possible triangles that can be constructed. Hence congruence cannot be guaranteed between two triangles with the same SSA dimensions.
Josh rented a truck for one day there was a base fee fee of $12 and there was additional charge of 8 cents for each mile driven the total cost (c) for driving x miles is given by the following function
C(x)=12.00+0.08x
what is the total rental cost if Josh drive 20 miles?
Answer:
$13.60
Step-by-step explanation:
You want to evaluate the rental cost function C(x) = 12.00 +0.08x for x = 20.
EvaluationPut the value for x where x is in the cost function and do the arithmetic.
C(x) = 12.00 +0.08x
C(20) = 12.00 +0.08·20 = 12.00 +1.60
C(20) = 13.60
The total rental cost if Josh drives 20 miles is $13.60.
1. Which subset of real numbers does
√3 belong to?
The subset of real numbers √3 belong to is irrational numbers
What is a subset ?
If all of the items in a set A are also in a set B, then the sets A and B are subsets of one another. To put it another way, the set A is contained within the set B. A and B stand for the subset connection.
When all the components of Set A are also present in Set B, Set A is said to be a subset of Set B. Alternatively said, Set B contains Set A. Example: If set A contains X and Y and set B contains X, Y, and Z, then set A is a subset of set B because set B also contains X and Y.
As √3 is irrational number
∴it is a subset of real numbers √3 belong to is irrational numbers
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Graph the arithmetic sequence. -15,0,15,30
To graph a sequence, let a term's position number [tex]n[/tex] in the sequence be [tex]x[/tex]value.
What is an arithmetic sequence?An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. An arithmetic progression is another name for an arithmetic sequence.
Starting with a number and repeatedly adding a fixed constant (d) to it is an easy technique to create a series. An arithmetic sequence is this kind of sequence.
Definition: A sequence of the form a, a + d, a + 2d, a + 3d, a + 4d, etc. is an arithmetic sequence.
The term [tex]a_{n}[/tex] is the corresponding y value
Plot the ordered pairs
Make a table then plot the ordered pairs ([tex]n, a_{n}[/tex])
Position, [tex]n[/tex] Term, [tex]a_{n}[/tex] ([tex]n, a_{n}[/tex])
1 -15 (1, -15)
2 0 (2, 0)
3 15 (3, 15)
4 30 (4, 30)
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the mean score on a college placement exam is 500 with a standard deviation of 100. ninety-five percent of the test takers score below what value?
The value for which test score is below 95% percent for the given mean and standard deviation on a college placement is equal to 696.
As given in the question,
Given : 95% of the test takers score are below z.
z-score is given by,
z=(x-μ)/σ
Mean of the score 'μ' = 500
Standard deviation of the score ' σ' = 100
Z = 95%
= 0.95
P(z<Z) = 1-0.95
= 0.05
The value of z which corresponds to 0.05 in the table is equal to 1.96.
Substitute all the values we get,
z=(x-μ)/σ
⇒1.96 = ( x - 500 ) / 100
Multiply by 100 both the sides we get,
⇒ 196 = ( x - 500 )
⇒ x = 696
Therefore, the value for which test score is below 95% percent for the given mean and standard deviation is equal to 696.
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When Mr Norman turns 58, he will be two years older than twice the age his daughter will turn in January. How old is Nicole now?
How do I write down the equation?
Step-by-step explanation:
When Mr Norman turns 58, he will be two years older than twice the age his daughter will turn in January. How old is Nicole now?
equation: 58 = 2d + 2
58 = 2d + 2
subtract 2 from both sides:
56 = 2d
divide both sides by 2:
d = 28 , so his daughter is 28 years old.
(5/6z+5) + (-1/2-4)?
.
Answer: [tex]\frac{5}{6}z+\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]\frac{5}{6}z+5-\frac{1}{2}-4\\\\\frac{5}{6}z+1-\frac{1}{2}\\\\\frac{5}{6}z+\frac{1}{2}[/tex]
The ratio of yellow marbles to purple marbles was 13 to 4. If there were 102 marbles in the bag, how many were yellow marbles?
The number of yellow marbles based on the given ratio will be 78.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Suppose, the number of yellow marbles is Y while purple marbles are P.
As per the given,
The ratio Y/P = 13/4
Total Y + P = 102
(13/4)P + P = 102
13P + 4P = 408
17P = 408
P = 24
And, Y = 102 - 24 = 78
Hence "The number of yellow marbles based on the given ratio will be 78".
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- 5(-4) +3(5)| = ?
A. -35
B. -5
C. 5
D. 35
E. 36
please i need help
19. find the dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 10 cm. what is the maximum volume?
A right circular cylinder with the largest volume that can fit within a sphere with a 10 cm radius will have a maximum radius of 8.165 cm and a maximum height of 11.55 cm. Additionally, the largest volume is 2417.82 cm³.
What is cylinder?A cylinder is a three-dimensional solid in mathematics that maintains, at a given distance, two parallel bases connected by a curving surface. These bases often have a circular form (like a circle), and a line segment known as the axis connects the centers of the two bases. The height of the cylinder is "h," while the radius of the cylinder is "r," measuring the distance from the axis to the outside surface.
Here,
radius=10 cm
r²+h²/4=10²
r²=10²-h²/4
volume=πr²h
=π(10²-h²/4).h
V=π(10²h-h³/4)
dV/dh=π(10²-3h²/4)
dV/dh=0
10²=3h²/4
10²*2²/3=h²
20/√3=h
h=11.55 cm
r²=10²-h²/4
=10²-(10²*2²/3)/4
r²=(100-400/12)
r²=100-33.33
r²=66.67
r=√66.67
r=8.165 cm
volume=πr²h
=3.14*8.165*8.165*11.55
volume=2417.82 cm³
The dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 10 cm will be 8.165 cm radius and 11.55 cm height. Also the maximum volume is 2417.82 cm³.
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Write the equation of 5x-y=15 after it is reflected in the y-axis and then translated (3 -1)
Answer: y=-5x-1. I need someone to tell me what translating equations is and how to get there.
The equation after the transformation is y = -5x - 1
How to determine the equation after the transformation?From the question, we have the following parameters that can be used in our computation:
Equation: 5x - y = 15
Make y the subject
So, we have
y = 5x + 15
The rule of reflection across the y-axis is
(x, y) = (-x, y)
So, we have the following equation
y = -5x + 15
The rule of translation by (3 -1) is
(x, y) = (x + 3, y - 1)
So, we have the following equation
y = -5(x + 3) + 15 - 1
Expand
y = -5x - 15 + 15 - 1
So, we have
y = -5x - 1
Hence, the equation is y = -5x - 1
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What is the value of the expression 32.4 ÷ 6?
Group of answer choices
4.4
5.4
6.4
7.4
Answer:
If you divide 32.4 by 6, then you get 5.4 as an answer
9. Sales: $50,000
Returns: $4,680
Net Sales: (a)
Cost of goods sold: $22,950
Gross profit: (b)
The gross profit of the Blog Inc would be $22,370.
What is gross profit?Gross profit is the profit of a company or an entity after subtracting all the costs that are related to manufacturing and selling its products or services. Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that Sales: $50,000
Returns: $4,680
Cost of goods sold: $22,950
Therefore,
Net Sales: 50,000 - 4,680
= 45,320
We can calculate the Gross Profit;
Gross Profit = (Net Sales – Cost of Goods Sold)
= ($45,320- $22,950)
= $22,370
Hence, the gross profit would be $22,370.
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Evaluate using the given values.
Answer:
8
Step-by-step explanation:
x^3/3-y
3^3/3-1
27/3-1
9-1
8
Hopes this helps please mark brainliest
A student's course grade is related to class attendance. The grade can be modeled by the equation ý = 0. 66x +33. 3, where ŷ is the student's grade as a percentage
and x is the number of days that the student attended class. For a student who was in attendance for 90 days and has a grade of 94%, find and interpret the residual.
-1. 3; The regression line underpredicts the student's class average.
1. 3; The regression line overpredicts the student's class average.
-1. 3; The regression line overpredicts the student's class average.
1. 3; The regression line underpredicts the student's class average.
For the given modeled of equation ý = 0.66x + 33.3 the interpretation of the residual is given option D. 1.3 The regression line underpredicts the students class average.
As given in the question,
Equation to represents the grade of a students based on class attendance is given by :
ý = 0.66x + 33.3
Where ý is the grade of students in form of percentage.
And 'x' is the students attendance
Actual percentage = 94% when x = 90
Predicted percentage is,
ý = 0.66(90) + 33.3
= 92.7%
Residual = Actual - Predicted
= 94% - 92.7%
= 1.3
Actual > Predicted
Therefore, from the given equation the interpretation of the residual is given by Option D. 1.3 student's class average was underpredicted by the regression line.
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Answer:
DDDDDDDDDD
Step-by-step explanation:
please mark as brainliest please!!!!!!!
I need help on my test please help its 7th grade Im just bad at math
For the given inequality 14 - 3f > 2 the option that comes out be correct is
f < 4 i.e option 2.
What is inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.The majority of the time, size comparisons between two numbers on the number line are made.
Here, "Less than" and "Greater than" have new meanings.
Less-than sign is the symbol for such phrase.
14 - 3f > 2
adding 3f on both sides:
14 - 3f + 3f > 2 + 3f
14 > 2 + 3f
subtracting 2 on both sides:
14 - 2 > 2 + 3f - 2
12 > 3f
dividing 3 on both sides:
(12)/3 > (3f)/3
4 > f
which means f < 4
Therefore, option 2 is correct.
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What is the equation in slope-intercept form of the line that passes through the point (4, 7) and is parallel to the line represented by y = 2x - 5?
Step-by-step explanation:
please see the attachment