If Carol’s final grade is a 91, Carol's lowest test score was 82.
Given;
Average in 9 tests = 90
Average when the lowest score is removed = 91
How to calculate the average?The average or Mean is calculated as thus;
Average = [tex]\dfrac{\sum x}{n}[/tex]
Where the summation of x is the sum of test scores.
n = number of tests
n = 9 - 1 = 8 and average = 91
91 = [tex]\dfrac{\sum x}{8}[/tex]
[tex]\sum x = 91 \times 8\\\\\sum x = 728[/tex]
Thus, Carol's test score in 8 subjects is 728
Let's consider the 9th subject represent the subject Carol had the least score.
n = 9
Average = 90
Average = 728 + the 9th subject
Multiply both sides by 9
90 x 9 = 728 + the 9th subject
810 = 728 + the 9th subject
Subtract 728 from both sides
810 - 728 = 728- 728 + the 9th subject
82 = the 9th subject
Hence, Carol's lowest test score was 82.
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How many different three-digit numbers can be written using digits from the set 2, 3, 4, 5, 6 without any repeating digits? A. 10 B. 120 C. 20 D. 60
the second statement is the blank of the first x ⇒ y ¬x = ¬y
The second statement is the inverse statement of the first conditional statement.
What is the second statement?If x and y are two propositions, then:
x ⇒ y
Is a conditional statement:
"If x, then y".
The other statement is:
¬x ⇒ ¬y
Where:
¬x means "not x"
So the statement is:
"If not x, then not y".
That would be the inverse statement of the given conditional statement.
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a car travels 87 miles north and 114 miles west. what is the magnitude of the cars resultant vector
The magnitude of the resultant vector is 27 miles
How to determine the vector magnitudeResultant vector = Distance of A - Distance of B
This is so because of the opposite direction of the car's movement
A = 87 miles
B = 114 miles
Resultant vector = 114 - 87
Resultant vector = 27 miles
Thus, the magnitude of the resultant vector is 27 miles
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Please help me understand how to do the problem and what the answer is
The force required to move the object by 15 feet will be 48 lbs.
What is force?The effort or an external agent responsible for moving or stopping any object is called a force. It is given that the force required to move the object at the distance of 9 feet is 80 lbs we need to calculate the force required to move the object by 15 feet.
The force will be calculated. We can make an equation from the given data in the question:-
[F1/F2] = [d2/d1]
F2 = [F1 x d1 ] / [d2]
F2 = [ 80 x 9 ] / [ 15 ]
F2 = a
Therefore the force required to move the object by 15 feet will be 48 lbs.
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Match the vocabulary word to its correct definition.
1. constant -----a mathematical phrase that cannot be determined true or false
2. coefficien-------- a mathematical expression containing one or more variables
3. variable------- the constant preceding the variables in a product
4. expression---- a numerical value
5. algebraic expression------- a letter or symbol used to represent an unknown
Answer:
Constant: A numerical value
Coefficient: The constant preceding the variables in a product
Variable: a letter or symbol used to represent and unknown
Expression: A mathematical phrase that cannot be determined by true or false
Algebraic expression: A mathematical expression containing one or more variables
Step-by-step explanation:
A pyramid has 24 edges and 13 faces, find the number of vertices in the figure -geometry
Answer: 13 vertices
Step-by-step explanation:
We can use the following formula to find the number of vertices in the figure. V is the number of vertices, F is the number of faces, and E is the number of edges.
V = 2 - F + E
V = 2 - (13) + (24)
V = 13
Which of the following equations have no solutions? Choose all answers that apply: (Choice A) 40x+40=40x+20 (Choice B) 20x+40=40x+20 (Choice C) -20x+40=-20x+20 (Choice D) −40x+40=20x+20
The answer choice in which case the equation has no solution are; Choice A ; 40x+40=40x+20 and Choice C; -20x+40=-20x+20.
Which of the following equations have no solutions?A system of linear equations is determined to have no solutions when the variable coefficients diminish upon evaluation and hence, the value of the variable can not be determined.
Hence, Choices A and C; in which case; the coefficients of variable X amount to 0 upon evaluation are equations with no solution.
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Can someone help me with these problems and can you number them
The correlation is a negative correlation, because weights and city MPG do not increase at the same time
The graph of the table of valuesTo graph of the table of values, we plot
The weights on the x-axisThe city MPG on the y-axisSee attachment for graph
Type of correlationThe correlation is a negative correlation, because weights and city MPG do not increase at the same time
The equation of the line of best fitTo do this, we make use of a graphing calculator.
From the graphing calculator, we have the following summary:
Sum of X = 463Sum of Y = 388Mean X = 28.9375Mean Y = 24.25Sum of squares (SSX) = 862.9375Sum of products (SP) = -857.75The line of best fit equation is
y = bx + a
Where
b = SP/SSX = -857.75/862.94 = -0.99
a = MY - bMX = 24.25 - (-0.99*28.94) = 53.0
So, we have:
y = -0.99x + 53
Hence, the equation of the line of best fit is y = -0.99x + 53
The weight for 30 MPGThis means that y = 30
So, we have:
-0.99x + 53 = 30
Subtract 53 from both sides
-0.99x = -23
Divide by -0.99
x =23
Hence, the predicted weight is 23 pounds
The city MPG for 1500 poundsThis means that x = 1500
So, we have:
y = -0.99 * 1500 + 53
Evaluate
y = -1432
Hence, the city MPG for 1500 pounds is -1432
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Which equation represents a graph with a vertex at (–3, 2)?
The equation represents a graph with a vertex at (–3, 2) is y = a(x + 3)² + 2
Vertex of a functionThe standard vertex of a function is given as shown below
y = a(x - h)² + k
where (h, k) is the vertex of the function
Given the vertex of a function at (-3, 2). On substituting, we will have:
y = a(x - (-3))² + 2
y = a(x + 3)² + 2
Hence the equation represents a graph with a vertex at (–3, 2) is y = a(x + 3)² + 2
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^
4. A list of numbers is given below. If x is a number
in this list, which inequality could represent x?
{-5, -12,-2,-9}
A. x < -13
B. x < -1
C. x>-12
D. x < -2
Answer:
B. x < -1
Step-by-step explanation:
Hello!
Let's put them in order from greatest to least:
[tex]\{-2,-5,-9,-12\}[/tex]Given our possible inequalities, we need to find the inequality that contains all of these values.
The inequality that works is x < -1, as all values are less than -1.
Therefore, the answer is B. x < -1.
How does this graph change between point D and point G?
A graph increases from point D to point G, and then decreases.
The graph increases.
The graph decreases.
The graph increases, then decreases.
The graph remains constant.
Answer:
The graph increases.
Step-by-step explanation:
hope this helps!!
Answer: the graph increases
Step-by-step explanation: did test
The growth of the population over the years in a small town is represented by the
function: () = 3548 (0. 87)
Based on the given population function, the population of the town can be said to be increasing.
How do we know the population is increasing?The population of the town is increasing because the value of "b" is positive and greater than one.
"b" which in this case is 0.87, is the rate at which the population is growing overtime. If it is a positive figure, then the population is expanding.
The question is:
Is the town's population increasing or decreasing?
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[tex]if a= \sqrt{3}+5/\sqrt{3}-5 and b= \sqrt{3}-5/\sqrt{3}+5 then find a^2 - b ^2[/tex]
The result of the evaluation as demanded in the task content is; -40 - 80√3.
What is the value of a²-b²?The expression; a² - b² can be evaluated by means of difference of two squares as follows;
a² - b² = (a+b)(a-b)
Therefore, we have;
= ((√3 +5√3 -5) + (√3 -5√3 -5)) ((√3 +5√3 -5) - (√3 -5√3 -5))
= (2√3 -10)(10√3 +10)
= 60 - 80√3 -100
= -40 - 80√3.
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Differentiation question, please explain :)
The Logistic Law of Population Growth, first proposed by Belgian mathematician
Pierre Verhulst in 1837, is given by [tex]\frac{dN}{dt}= kN-bN^2[/tex], where k and b are constants.
Show that the equation [tex]N= \frac{KN0}{nMN0+(k-bN0)e^{-kt} }[/tex] is a solution of this differential equation (N0 is a constant).
Answer:
dN)/(dt)=(rN(K-N))/K is the answer.
Step-by-step explanation:
The logistic equation (sometimes called the Verhulst model or logistic growth curve) is a model of population growth first published by Pierre Verhulst.
The continuous version of the logistic model is described by the differential equation is:
(dN)/(dt)=(rN(K-N))/K. (where r is the Malthusian parameter (rate of maximum population growth) and K is the so-called carrying capacity (i.e., the maximum sustainable population).
So, the correct option is ' (dN)/(dt)=(rN(K-N))/K'.
Mark as brainlist pls!
What is the domain of the sine and cosine functions?
Answer:
domain of the sine and cosine functions is all real numbers
Step-by-step explanation:
range of both the sine and cosine functions is [−1,1]
graph can go left and right to infinity
graph goes up and down between 1 and -1
graph looks like a wave or
like U letters next to each other
UUUU
sine and cosine of an angle have the same absolute value as the sine and cosine of its reference angle.
mathlibretextsorg
The question is on the picture
Answer: 68
Step-by-step explanation:
By the inscribed angle theorem, arc BA measures twice of 34 degrees, which is 68 degrees.
how would you solve this question?
How many solutions does 6 -3x = 12 - 6x have?
Answer:
x = 2
Only 1 solution
Step-by-step explanation:
6 - 3x = 12 - 6x
3x = 6
x = 2
The side lengths of a 30-60-90 triangle are in the ratio 1:square root :2. What is the cos 60°?
A.square root 3
B.1/2
C.square root 3/2
D.square root 3/3
Pls don’t get this taken down, will give brainlest!!
By what factor should -1 - 4i/ 2 + 9i be multiplied to find the quotient? Enter any complex numbers in the form a + bi
The factor by which the complex rational number be multiplied is; 2 -9i.
What value should be used to multiply to find the quotient?The expression given in the task is a fraction made up of complex numbers.
Hence in a bid to evaluate the quotient of the expression; -1 - 4i/ 2 + 9i.
The numerator and denominator must be multiplied by the conjugate of the denominator which in this case is; 2 -9i.
This is to help reduce the denominator to a real number.
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4. 5. a) b) c) a) When the cost of 7kg of sugar is Rs 490, find the cost of 12 kg of sugar. If the cost of 5m of cloth is Rs 375, find the cost of 80m of cloth. If the cost of 70kg of rice is Rs 5600, find the cost of 1 quintal of rice. The cost of cloth com of 4 . 5 . a ) b ) c ) a ) When the cost of 7kg of sugar is Rs 490 , find the cost of 12 kg of sugar . If the cost of 5m of cloth is Rs 375 , find the cost of 80m of cloth . If the cost of 70kg of rice is Rs 5600 , find the cost of 1 quintal of rice . The cost of cloth com of
Answer:
B
Step-by-step explanation:
i took the test
is there exactly one triangle that can be found using the given measurements
The correct option is B. Yes, SSS congruency
Reasons
Yes, more than one triangle can be made using the given measurements
The appropriate triangle congruence postulate is the SSS congruence which states that If all the three sides of one triangle are equivalent to that of the second triangle, then the two triangles are said to be congruent.
Thus, the option B is correct
The complete question is ;
The measurements of a triangle are given. Is there exactly one triangle that can be formed using the given measurements? If so, identify the appropriate triangle congruence postulate.
∆ABC : m ∠A = 90°, AB = 15, AC = 15
A)No, More than one triangle could be made with these measures
B)Yes, SSS congruency
C)Yes, ASA congruency
D)Yes, SAS congruency
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Can someone pls help me out on this, just fill in the blanks on the columns, it’s geometry btw. It’s urgent pls so ASAP!!
1) Isosceles [tex]\triangle ABC[/tex] with [tex]\overline{AC} \cong \overline{BC}[/tex], [tex]\overline{DE} \perp \overline{AC}[/tex], [tex]\overline{DF} \perp \overline{BC}[/tex], [tex]\overline{DE} \cong \overline{DF}[/tex] (given)
2) [tex]\angle CAB \cong \angle CBA[/tex] (angles opposite congruent sides in a triangle are congruent)
3) [tex]\angle AED[/tex] and [tex]\angle DFB[/tex] are right angles (perpendicular lines form right angles)
4) [tex]\angle AED \cong \angle DFB[/tex] (all right angles are congruent)
5) [tex]\triangle DEA \cong \triangle DFB[/tex] (AAS)
6) [tex]D[/tex] is the midpoint of [tex]\overline{AB}[/tex] (if a point splits a segment into two congruent parts, it is a midpoint)
PLEASE HELP ME
Which are dependent events? Check all that apply.
•choosing 2 socks from a drawer, •without replacement
•flipping a coin 4 times
•picking 4 cards from a deck, •one after the other
•rolling a number cube twice
•spinning a spinner and rolling a number cube
The dependent events are:
choosing 2 socks from a drawer, without replacementpicking 4 cards from a deck, one after the other.Which events are dependent?Two events are dependent when the outcome of the first event affects the probabilities for the outcomes of the second event.
The first pair:
"choosing 2 socks from a drawer, without replacement"
Is a pair of dependent events. Because the first pair chosen can't be chosen on the second event. Then, the outcome of the first event affects the second event.
The third option:
"picking 4 cards from a deck, one after the other"
Again, here we have dependent events, because the cards already picked can't appear in the next events.
The other 3 options are sets of independent events.
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A cylinder has a cross-sectional area of 17m² and a length of 14 m what is the volume of the cylinder
Answer:
your answer please mark me as brainlist
Step-by-step explanation:
V
=
238
m³
A company has 12 000 employees. During the financial crisis in 2008, 2.5 % of them were retrenched
50.75 % of them had a pay cut and the rest were unaffected. Find the number of employees who
were unaffected by the financial crisis.
Answer:
5610
Step-by-step explanation:
unaffected people will be (100%-2.5\%-50.75%)=46.75% of 12000:
[tex]12000\cdot 46.75\%=12000\cdot \frac{46.75}{100} =120\cdot 46.75=5610[/tex]
How many solutions are there to the equation below?
√x = -7
Answer:
There are no solutions.
Step-by-step explanation:
Hope this helped! :D
HELP HELP HELP
Quick algebra 1 question for 50 points!
1. Provide a brief overview of graphing a linear equation using slope.
2. Create 2 original problems and solve it using the graphing a linear equation using slope method, show your work as you solve the problem and explain each step.
The standard equation of a straight line is given by y = mx + b, where m is the slope (rate of change) and b is the y intercept of the line.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The standard equation of a straight line is given as:
y = mx + b
Where m is the slope (rate of change) and b is the y intercept of the line.
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g = 15 - m/32
Alice fills up the gas tank of her car before going for a long drive, the equation above shows the amount of gas in gallons in Alice's car when she has driven m (miles). What does 32 mean in the equation?
The value of 32 in the equation will serve as the time taken by the driver to travel
Functions and valuesIf Alice fills up the gas tank of her car before going for a long drive, and the equation that shows the amount of gas in gallons in Alice's car when she has driven m (miles). is given as:
g = 15 - m/32
The value of 32 in the equation will serve as the time taken by the driver to travel
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soybeans have a conversion factor of 36.744 (bu/t). how much do 45 bushels weight. Show your work pls
By using unit conversion and direct proportionality model, we find that 45 bushels of soybeans are equal to a weight of 1.225 tonnes.
How many tonnes are a given quantity of bushels?
In this question we have an application of direct proportionality model, whose form is shown below:
y = k · x (1)
Where:
x - Quantity of bushelsk - Conversion rate, in tonnes per bushel.y - Quantity of tonnesIf we know that x = 45 bu and k = 1/36.744, then the soybean quantity in tonnes is:
y = (1/36.744 t/bu) · (45 bu)
y = 1.225 t
By using unit conversion and direct proportionality model, we find that 45 bushels of soybeans are equal to a weight of 1.225 tonnes.
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help me please im stuck here
The reciprocal relationship of the graph is graph (a)
How to determine the reciprocal relationship?The reciprocal relationship implies that:
The x and the y axes are swapped.
When the x and the y axes are swapped, the value on both axes swap their positions
For the given graph, the reciprocal relationship is graph (a)
This is shown in the attached graph
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