Answer:
There were 20 questions on the quiz
Step-by-step explanation:
In this question, we are concerned with knowing the number of questions on a quiz, given that Deana had a certain percentage after scoring an amount of marks.
We proceed as follows;
Let the number of questions on the quiz be X.
Now, she got 85% by making 3 incorrect choices. This means the percentage of questions she got incorrectly would be 100-85 = 15%
what we are saying is that it is just 15% of her questions that were wrong.
This mathematically;
15% of x = 3
15/100 * x = 3
15x = 3 * 100
15x = 300
x = 300/15
x = 20
Find the product of z1 and z2, where z1 = 5(cos 60° + i sin 60°) and z2 = 7(cos 210° + i sin 210°)
Write in a + bi form
The product of the two complex numbers are 35[Cos270 + i Sin(270)].
What is a complex function?The function which is made up of the real numbers, as well as imaginary numbers, are called complex numbers these numbers are represented by a +ib form where the first part is the real part and the second part is the imaginary form.
The product of the two complex numbers will be done as:-
[tex]z_1z_2=r_1r_2Cos (\theta_1+\theta_2)+iSin(\theta_1+\theta_2)[/tex]
[tex]z_1z_2= 5\times 7[Cos(60+210)+iSin(60+210)][/tex]
[tex]z_1z_2=35[(Cos270)+iSin(270)][/tex]
Therefore the product of the two complex numbers is 35[Cos270 + i Sin(270)].
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N a soccer game, Sally kicks the ball to a teammate who is on the other side of the field. The ball's height h (in feet above the ground), t seconds after Sally kicked it, is modeled by: -2t^2+10t What is the height of the ball at the time it is kicked?
Answer:
At the time that it is kicked, the ball is on the ground, that is, it's height is 0 feet.
Step-by-step explanation:
The height of the ball after t seconds is given by the following equation:
[tex]h(t) = -2t^{2} + 10t[/tex]
What is the height of the ball at the time it is kicked?
The ball is kicked at t = 0.
So we have to find h(0)
[tex]h(0) = -2*0^{2} + 10*0 = 0[/tex]
At the time that it is kicked, the ball is on the ground, that is, it's height is 0 feet.
The value of Q is given by the relation Q = 17m. If m is an integer greater than 15 and less than 23, then which of the following is the value of Q?
complete question:
The value of Q is given by the relation Q = 17m. If m is an integer greater than 15 and less than 23, then which of the following is the value of Q?
A. 255
B. 290
C. 306
D. 391
Answer:
C. 306
Step-by-step explanation:
The equation is Q = 17m. m is an integer and it is greater than 15 and less than 23 . This means m can only be 16, 17, 18, 19, 20, 21 and 22.
Insert any of the value of Q from the options in the equation Q = 17m and solve the equation. The answer of m must be between 16 to 22.
let us try
option A
Q = 17m
255/17 = m
m = 15 (not A since it not greater than 15)
option B
Q = 17m
290/17 = m
m = 17.0588235294
(not an integer)
option C
Q = 17m
306/17 = m
m = 18
(correct . it is an integer and greater than 15 and less than 22)
option D
Q = 17m
391/17 = m
m = 23
(not less than 23)
the temperature was -6 f. it rose so that the temperature was 0 f. what represents the change in temperature
Answer:
f + 6
Step-by-step explanation:
The change in temperature is 6 f.
Given,
The temperature was -6 f.
It rose so that the temperature was 0 f.
We need to find what represents the change in temperature.
Initial temperature = -6 f.
Final temperature = 0 f.
Let the change in temperature be M.
Now,
We have,
It rose so that the temperature was 0 f.
So we can write it as,
Initial temperature + M = final temperature
-6 f + M = 0 f
-6 f + M = 0
M = 0 + 6 f
M = 6 f.
Thus we see that the change in temperature is 6 f.
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answer quick for brainliest...
Answer:
D. y=25
Step-by-step explanation:
Answer:
The answer is D.
Step-by-step explanation:
You have to substitute x = 5 into the equation of y :
[tex]y = 5x[/tex]
Let x = 5,
[tex]y = 5(5)[/tex]
[tex]y = 25[/tex]
Given sin A = 12/13 and that angle A is in Quadrant 1,
find the exact value of cot A in simplest radical form
using a rational denominator.
We have been given that [tex]\text{sin}(A)=\frac{12}{13}[/tex] and angle A is in quadrant 1. We are asked to find the exact value of [tex]\text{cot}(A)[/tex] in simplest radical form.
We know that sine relates opposite side of right triangle with hypotenuse.
[tex]\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]
This means that opposite side is 12 units and hypotenuse is 13 units.
We know that cotangent relates adjacent side of right triangle with adjacent side.
[tex]\text{cot}=\frac{\text{Adjacent}}{\text{Opposite}}[/tex]
Now we will find adjacent side using Pythagoras theorem as:
[tex]\text{Adjacent}^2=\text{Hypotenuse}^2-\text{Oppoiste}^2[/tex]
[tex]\text{Adjacent}^2=13^2-12^2[/tex]
[tex]\text{Adjacent}^2=169-144[/tex]
[tex]\text{Adjacent}^2=25[/tex]
Let us take positive square root on both sides:
[tex]\sqrt{\text{Adjacent}^2}=\sqrt{25}[/tex]
[tex]\text{Adjacent}=5[/tex]
Therefore, adjacent side of angle A is 5 units.
[tex]\text{cot}(A)=\frac{5}{12}[/tex]
Therefore, the exact value of cot A is [tex]\frac{5}{12}[/tex].
The exact value of cot(A), where sin(A) is 12/13 and angle A is in Quadrant 1, is 5/12 in simplest radical form with a rational denominator.
To find the exact value of cotangent (cot) of angle A when sin A is given as 12/13, you can use the trigonometric identity:cot(A) = 1 / tan(A)Now, you need to find the value of tan(A). In Quadrant I, where angle A is located, both sine (sin) and tangent (tan) are positive.You are given that sin(A) = 12/13. To find tan(A), you can use the relationship between sin, cos, and tan:tan(A) = sin(A) / cos(A)You can use the Pythagorean identity for sine and cosine in right triangles:sin²(A) + cos²(A) = 1Since sin(A) is given, you can solve for cos(A):cos(A) = √(1 - sin²(A)) = √(1 - (12/13)²) = √(1 - 144/169) = √(25/169) = 5/13Now that you have both sin(A) and cos(A), you can find tan(A):tan(A) = sin(A) / cos(A) = (12/13) / (5/13) = 12/5Finally, you can find cot(A) by taking the reciprocal of tan(A):cot(A) = 1 / tan(A) = 1 / (12/5) = 5/12So, the exact value of cot(A) in simplest radical form using a rational denominator is 5/12.For more questions on rational denominator -
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Find the length of a rectangle if the Area is 27 cm squared and the width is 3 cm
Answer: The length is 9.
Step-by-step explanation: 27/3=9
The original price of a new computer is $233.00. If the computer is marked down 32%, what is the new price?
Answer:
= $ 158.44
Step-by-step explanation:
$ 233 = 100%
100% - 32% = 68% which is the percentage that represents the new price
If 100% = $ 233
What about 68% = $?
= (68 x 233) ÷ 100
= 15844 ÷ 100
= $ 158.44
Waffles are made with 2 1/2 cups water and 1 1/2 cups milk. What is the ratio of water to milk?
Answer:
5 : 3
Step-by-step explanation:
Water: 2.5 cups
Milk: 1.5 cups
Water/Milk: 2.5/1.5 = 5/2 / 3/2 = 5/2 * 2/3 = 5/3
Hope this helps :)
The ratio of water to milk in the waffles will be 5 : 3.
What is ratio?The quantitative relation between two amounts showing the number of times one value contains or is contained within the other.
Given is that waffles are made with 2 1/2 cups water and 1 1/2 cups milk.
We can write the given mixed fractions as proper fractions -
2[tex]\frac{1}{2}[/tex] = 5/2 = W
1[tex]\frac{1}{2}[/tex] = 3/2 = M
Now, we can write the ratio of water to milk as -
[W]/[M] = (5/2)/(3/2) = 5/2 x 2/3 = 5/3
Therefore, the ratio of water to milk in the waffles will be 5 : 3.
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-7d - 3 = 11
what's the answer please
Answer:
-2
Step-by-step explanation:
add 3 to 11 and then divide 14 by -7
Answer:
d = -2
Step-by-step explanation:
-7d - 3 = 11
-7d = 11 + 3
-7d = 14
d = 14/-7
d = -2
hope it helps!
If five times four is thirty-three, what will the fourth of twenty be?
Final answer:
The student's question appears to involve a play on words or a riddle, but using standard mathematics, the fourth of twenty is calculated by dividing twenty by four, which equals five.
Explanation:
The question appears to be a puzzle rather than a straightforward mathematical problem. Given the statement that 'five times four is thirty-three' is not mathematically correct (since 5 × 4 = 20), it suggests that there's an error or play on words. The most likely solution for 'what will the fourth of twenty be?' using standard mathematics is 5, because normally one would divide twenty by four to get this result. However, if we are following the same logical pattern as in the incorrect statement 'five times four is thirty-three', we might question whether 'the fourth of twenty' should similarly be an unconventional result. Without more context, we stick with the conventional approach.
Identify the Y intercept using the graph below
Answer:
-2 is the answer
Step-by-step explanation:
the x-axis is the horizontal line, while the y-axis is the vertical line. and the point is -2
Answer:
-2
Step-by-step explanation:
The y-intercept is where the line crosses the y axis.
Which statement is true?
A. 60 cL = 600 dL
B. 60 kL = 0.06 L
C. 60 dL = 6000 mL
D. 60 hL = 60000L
Answer:
C. 60 dL = 6000 mL
60 x 100 = 6000
Step-by-step explanation:
Formula: multiply the value by 100
Final answer:
The statement that is true is D, which correctly states that 60 hectoliters are equal to 60000 liters, as 1 hectoliter equals 1000 liters.
Explanation:
The student has asked which statement is true regarding the comparison of different units of volume measurement. Only one of the statements given represents an accurate conversion:
Answer D
60 hectoliters (hL) equals 60000 liters (L). This is true because 1 hectoliter is equivalent to 1000 liters. Hence, if we have 60 hectoliters, we multiply 60 by 1000 to find the conversion in liters:
60 hL * 1000 L/hL = 60000 L
Therefore, statement D is correct.
Michael is drawing a card from a standard deck of 52 cards, which includes 4 aces: the ace of clubs, the ace of diamonds, the ace of hearts, and the ace of spades. For each trial, he draws a card, records which card he drew, and returns it to the deck. He draws an ace 312 times. Of the times he draws an ace, which of the following would be a good estimate for the number of times the ace drawn is the ace of hearts?
Final answer:
Michael is drawing cards from a deck with replacement. Since all aces are equally likely to be drawn, we can divide the total number of aces drawn by the number of different aces to estimate that the ace of hearts would likely be drawn 78 times out of the 312 instances of drawing an ace.
Explanation:
When Michael draws an ace from a standard deck of 52 cards, there are 4 aces available (one from each suit: clubs, diamonds, hearts, and spades). If Michael is drawing a card, recording it, and returning it to the deck (which means each draw is an independent event with replacement), the probability of drawing any specific ace, such as the ace of hearts, is the same for each draw.
Since Michael draws an ace 312 times and there are 4 equally likely aces he could draw, we can estimate the number of times he would draw the ace of hearts by dividing the total number of aces drawn by the number of different aces:
Number of times drawing the ace of hearts = Total number of aces drawn ÷ Number of different aces = 312 ÷ 4 = 78.
Therefore, a good estimate for the number of times the ace of hearts was drawn is 78 times.
The cell phone company decided to collect similar data but this time they collected information of texting speed according to age. Use the process of creating a scatter plot to describe how to create a scatterplot of the new data.
Step-by-step explanation:
As we know, Scatter plots resembles line graphs in that they are plotted on the x and y axis and the purpose of a scatter plot is to shows if the variables are related to each other. If yes, they can draw a line of best fit which can expose or go through most of the points in the plot.
Given the information in the question, we know:
"they collected information of texting speed according to age"
=> We have 2 variables here which are age and (texting speed)
Step 1:
Label the x-axis the input variable (age) Label the y-axis the output variable (texting speed)Step 2: Plot the points according to age and texting speed
Hence, from that plot, it could have two cases in the relation of age and texting speed which are "the more time, more text is written", or "the less time, more text is written".
Answer:
Label axes according to input and output variables. Plot the ordered pair of the independent and dependent variable on the coordinate plane. Identify if there is a relationship between the variables.
Step-by-step explanation:
What is the area of a circle if the diameter is 6 centimeters?
Answer:
18pi or 56.52 if you substitute pi with 3.14
Step-by-step explanation:
Answer:
[tex]28.26 {cm}^{2} [/tex]
Step-by-step explanation:
First let's find the radius
[tex]d = 2r \\ 6 = 2r \\ \frac{6}{2} = \frac{2r}{2} \\ 3 = r[/tex]
Now let's find the area.
[tex]\pi {r}^{2} \\ 3.14 \times 3 \times 3 \\ = 28.26 {cm}^{2} [/tex]
hope this helps
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good luck !have a nice day
GIVING AWAY A LOT OF POINTS!!
Using the information given, select the statement that can deduce the line segments to be parallel. If there are none, then select none.
When m∠2 = m∠ C
Answer:
None
Step-by-step explanation:
If Angles B and D were equal, then:
AB // CD
And
BC // AD
Since we don't have any such information, we can not call any of them parallel
5x+130 degrees and 8x+151 degrees answer asap plzzz!
Answer:
x = -7
Step-by-step explanation:
Simplifying
5x + 130 = 8x + 151
Reorder the terms:
130 + 5x = 8x + 151
Reorder the terms:
130 + 5x = 151 + 8x
Solving
130 + 5x = 151 + 8x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-8x' to each side of the equation.
130 + 5x + -8x = 151 + 8x + -8x
Combine like terms: 5x + -8x = -3x
130 + -3x = 151 + 8x + -8x
Combine like terms: 8x + -8x = 0
130 + -3x = 151 + 0
130 + -3x = 151
Add '-130' to each side of the equation.
130 + -130 + -3x = 151 + -130
Combine like terms: 130 + -130 = 0
0 + -3x = 151 + -130
-3x = 151 + -130
Combine like terms: 151 + -130 = 21
-3x = 21
Divide each side by '-3'.
x = -7
Simplifying
x = -7
At soccer practice, Hassan warms up by kicking balls at the goal. Yesterday, Hassan made 24 goals in 3 minutes. Today, he only spent 2 minutes kicking balls at the goal.
If Hassan made goals at the same rate, how many goals did he make today?
Answer:
Hassan scores 16 goals today if he scores at the same rate today.
Step-by-step explanation:
Hassan scores 24 goals in 3 minutes.
Here, unitary method can be used to calculate the number of goals scored today i.e. in 2 minutes.
Hassan's rate of scoring goals (Number of goals scored in a minute) is [tex]\dfrac{24}{3}[/tex].
Number of goals scored in a minute = 8 goals per minute
It is given that, today as well he is scoring at the same rate:
So, number of goals scored today in 2 minutes = [tex]8 \times 2 \Rightarrow 16[/tex] goals.
Hassan scored 16 goals today.
Please help me with this!
Answer:
Step-by-step explanation:
DE = LK {given that length of DE & LK are equal}
EF = JK {given that length of EF & JK are 8 cm}
DF = LJ { given}
ΔDEF ≅ ΔLKJ by SSS congruent
1
Given g(x) = 3x + 3, find g(6).
Answer:
21
Step-by-step explanation:
g(6)=3(6)+3
g(6)=18+3
g(6)=21
The value of g(6) is 12.
what is function?Function, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are ubiquitous in mathematics and are essential for formulating physical relationships in the sciences.
Given:
g(x) = 3x + 3
Now for x=3
g(3)= 3*3+3
=9+3
=12
Hence, the value of function is 12.
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What is the radius of a circle whose equation is (x + 5)2 + (y - 3)2 = 42?
0
O
2 units
4 units
8 units
16 units
0
Answer:
the answer is 8 units so that all i have to say.
The radius of a circle whose equation is (x + 5)^2 + (y - 3)^2 = 4^2 is mathematically given as
r=4 units, Option B is correct
What is the radius of a circle whose equation is (x + 5)^2 + (y - 3)^2 = 4^2?Question Parameters:
a circle whose equation is (x + 5)^2 + (y - 3)^2 = 4^2
Generally, the equation for the circle is mathematically given as
(x + 5)^2 + (y - 3)^2 = 4^2
Therefore, its standard form of a circle equation is
(x-h)^2+(y-k)^2=r^2
In conclusion, Comparing both equations
r^2=4^2
r=4
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A student council has nine officers, of which six are girls and three are boys. If two officers are chosen at random to attend a meeting with the principal, what is the probability that the first officer chosen is a girl and the second is a boy? please help
Final answer:
The probability that the first officer chosen is a girl and the second is a boy is 1/4.
Explanation:
To find the probability that the first officer chosen is a girl and the second is a boy, we can use the concept of dependent events.
When the first officer is chosen, there will be 6 girls left out of a total of 9 officers.
Therefore, the probability of selecting a girl as the first officer is 6/9.
After the first officer is chosen, there will be 3 boys left out of 8 officers. So, the probability of selecting a boy as the second officer is 3/8.
Since the events are dependent, we can multiply the probabilities of each event to get the probability of both events happening.
So, the probability of the first officer being a girl and the second officer being a boy is (6/9) * (3/8) = 1/4, which can also be written as 0.25 or 25%.
The local newspaper has letters to the editor from 70 people. If this number represents 5% of all of the newspaper's readers, how many readers does the newspaper have? The newspaper has blank readers.
Answer:
This shows us that there are 1400 readers.
Step-by-step explanation:
To work this out you would first need to find how many times 5% goes into 100%, You can do this by dividing 100 by 5, this gives you 20. This is because the whole amount is equivalent to 100%.
To work out the total number of readers you would multiply 70 by 20, this gives you 1400. This is because we know that 70 is equivalent to 5% and that 5% goes into 100% 20. So by multiplying 70 by 20 we are working out the total (100%), and that this shows us there are 1400 readers.
1) Divide 100 by 5.
[tex]100/5=20[/tex]
2) Multiply 70 by 20.
[tex]70*20=1400[/tex]
How is geometry fundamental to being a pediatrician?
Answer:
Pediatricians use numbers to calculate the patient's growth, they also use numbers to calculate the amount of liquid in a given shot or vaccine. Children's weight and height are measured in kilograms and centimeters. They also use math to change kilograms to pounds and centimeters to inches.
Step-by-step explanation:
Answer:
Conversions
Medications are prescribed using the metric system and Apothecary's Measure. The former uses grams and milliliters, while the latter is a medieval system using grains, scruples, drams, minims, fluid drams, fluid ounces, pints, quarts and gallons. Because the United States doesn't use the metric system, pediatricians must convert between these systems. Strong algebra skills are crucial, as mistakes in prescriptions can have catastrophic results.
Fractions
Much of a pediatrician's work involves taking accurate measurements. When measuring a patient's heart rate, pediatricians must know to divide the number of heart beats by the amount of time passed. They must know how to interpret blood pressure measurements, which are expressed as fractions. They may have to explain to a patient that body mass index, an important measure of health, is equal to his weight divided by his height squared. Equations
Specialists in pediatrics may require knowledge of more advanced mathematical concepts. Research pediatricians use math to analyze data for useful results. Those who work with complex internal systems, such as the cardiovascular system, use advanced equations and formulas to check on the status of organs. Pediatricians must also be able to communicate mathematical results to patients in language that is easily understood.
Other
Pediatricians regularly check the growth and development of patients. They develop growth charts, measure children's height and weight, and assess their overall development over time. They also use math to calculate how much medicine to administer in shots, measured in cubic centimeters or milliliters.
Find the area of the shaded section round your answer to the nearest whole number you must multiply by pi
A. 3 sq units
B. 2 sq units
C. 2.6 sq units
D. 7 sq units
Answer:
A
Step-by-step explanation:
So first you need to know the formula for the area of a segment of a circle which is... A = 0.5 × (θ - sinθ) × r²
*make sure that you do this question in RADIANS
You know that θ (the angle) is 90° which is equal to π/2 and the radius is 3, so from here you just plug in numbers to the equation.
A = 0.5 × ( π/2 - sin(π/2)) × 3²
A = 2.5685... sq units = 3 sq units
Maura has a part-time job wrapping gifts at a department store. A customer comes in and asks her to wrap a box. Whatever is inside that box feels like it weighs 50 pounds! The box is shaped like a cube that is 20 inches long on each side. What is the volume of the box?
Answer:
The volume of the box is [tex]8000 in^3[/tex]
Step-by-step explanation:
Since the box is shaped like a cube, the volume of the box is:
[tex]V = L^3[/tex]
where l = length of side of the box
The box is 20 inches long on each side, that means that L = 20 in.
Hence, the volume of the box will be:
[tex]V = 20^3 = 8000 in^3[/tex]
The volume of the box is [tex]8000 in^3[/tex].
To find the volume of a cube-shaped box with sides of 20 inches, you multiply the side lengths together, resulting in a volume of 800TatExplan0 cubic inches.
ation:The question is asking for the volume of a cube-shaped box. To calculate the volume of a cube, we use the formula V = a^3, where 'a' is the length of one side of the cube. In this case, each side of the box is 20 inches long. Therefore, the volume of the box is:
V = 20 inches × 20 inches × 20 inches = 8000 cubic inches.
A pencil holder contains only six blue pencils and three red pencils. If two pencils are drawn at random, what is the probability both are blue?
The probability that both pencils drawn from the pencil holder are blue is 5/12.
What is the probability?Probability is used to calculate the odds that an event would occur. The probability that the event would occur lies between 0 and 1.
The probability that both are blue = (number of blue pencils / total number of pencils) x (number of blue pencils / total number of pencils - 1)
6/9 x 5/8 = 5/12
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A set of average city temperatures in July are normally distributed
with a mean of 23.5 degrees Celsius and a standard deviation of 2 degrees
Celsius. The average temperature of the City of Van Nuys is 23 degrees
Celsius.
What percentage of average city temperatures are higher than that of the
City of Van Nuys?
a) 59.87%
b) 44.04%
C) 55.96%
d) 40.13%
Answer:
a) 59.87%
Step-by-step explanation:
Given that the mean temperature (μ) = 23.5°C and the standard deviation (σ) is 2 °C.
The z score is used in statistics to measure number of standard deviation by which the raw score is above or below the mean value, It is calculated using the equation:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
The average temperature of the City of Van Nuys is 23 degrees. The z score is
[tex]z=\frac{x-\mu}{\sigma}=\frac{23-23,5}{2} =-0.25[/tex]
P(x > 23) = P(z > -0.25) = 1 - P(z < -0.25) = 1 - 0.4013 = 0.5987 = 59.87%
So anyone know how to do these
Answer:
1) A
2) B
Step-by-step explanation:
The formula of rate of change from a certain number to another is
f(b) - f(a)
-----------
b - a
(i tried making a fraction if u couldnt tell)
Now substitute the values of x into the equation
(3*(-1) + 2) - (3*(1) +2)
----------------------------
-1 - 1
now combine everything together:
(-3+2) - (3+2)
------------------
-2
-1 - 5 -6 3
------- = ------- = ----
-2 -2
now do the same for the second question
(0^2 + 3) - (3^2 + 3) (3 - 12) -9 3
-------------------------- = ---------- = ---------- = ----- (answer choice B)
0 - 3 -3 -3