The value of [p] will be p = - 1.46. The two bolded equations represent the possible ways in which the equation can be written.
What is a expression? What is a mathematical equation? What do you mean by domain and range of a function?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.We have the following equations -
2.3p - 10.1 = 6.5p - 4 - 0.01p
2.3p - 10.1 = 6.49p - 4
2.3p - 10.1 + 4 = 6.49p
2.3p - 6.1 = 6.49p
4.19p = - 6.1
p = - 1.46
Therefore, the value of [p] will be p = - 1.46. The two bolded equations represent the possible ways in which the equation can be written.
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work out the area of this triangle
height=2.5cm
base=4.6cm
Answer:
5.75
Step-by-step explanation:
So first you would multiply 2.5*4.6 which is 11.5
Next you would divide 11.5/2 because a triangle is half of a square.11.5/2 is 5.75
Two shoppers bought meat at a supermarket deli. The first shopper bought 3 pounds of meat for $9.87. The second shopper bought 4 pounds of a meat that cost $1 more per pound than the meat the first shopper bought. How much did the second shopper pay?
Answer: $17.16 dollars
Step-by-step explanation:
first, you divide 9.87 by three which equals $3.29
then you add 1 which is $4.29
Finally, multiply it by 4 which is $17.16
Answer:$17.16
Step-by-step explanation:
You deposit $600 in a savings account. After 18
months, you check your statement and see that
you have earned $31.50 in interest. What is the
interest rate for your account?
Answer:
To calculate the interest rate for your account, you will need to use the formula for simple interest:
Interest = Principal x Rate x Time
In this case, the principal is the amount of money you deposited, or $600. The time is the number of months the money was in the account, or 18 months. And the interest is the amount of money you earned, or $31.50.
Plugging these values into the formula, we get:
$31.50 = $600 x Rate x 18
To solve for the rate, we can divide both sides of the equation by $600 and 18:
Rate = $31.50 / ($600 x 18)
Simplifying this expression gives us:
Rate = 0.01625
So, the interest rate for your account is approximately 1.625%.
A rectangular room is 2 meters longer than it is wide, and its perimeter is 20 meters. Find the dimension of
the room. Length and width
Answer:
Hope this helps good luck :)
see explanation
Step-by-step explanation:
Find relationship of length(L) and width(w)
Perimeter = L + W + L + W
[tex]20. = (w+2) + w + (w+2) +w 20. = 4w + 4 -4. -4 16 = 4w 16. = 4w 4. 4 4. = w w = 4 L. = w+2 = 4 +2 L = 6[/tex]
Answer width is 4 meters and length is 6 meters.
a population mean is 13. the sample mean is 12.8, and the sample standard deviation is two. the sample size is 20. what distribution should you use to perform a hypothesis test? assume the underlying population is normal.
To perform a hypothesis test we use students' t distribution.
What is a hypothesis test?
A statistical hypothesis test is a technique for determining if the available data are sufficient to support a specific hypothesis. We can make probabilistic claims regarding population parameters thanks to hypothesis testing.
Here, we have
Given, the population mean is 13. the sample mean is 12.8, and the sample standard deviation is two. the sample size is 20.
We have to find distribution to perform a hypothesis test.
The students t distribution is used when
1- sample size less than 30. Here 20.
2-population standard deviation not given.
3-population is normal.
Hence, we concluded that to perform a hypothesis test we use students' t distribution.
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A farm currently has 10 large male cattle. The farmer adds a pregnant rabbit to increase the livestock population. The novice farmer estimates that her rabbit population will double in size every month. Including the 10 cattle, how many animals will the farmer have after 7 months?
The number of animals will the farmer have after 7 months including the 10 cattle are 1280.
Explain the term rate of population growth?The country, territorial, or territorial area's average yearly rate of change in population size over a certain time period. It expresses the proportion, usually multiplied by 100, between the annual growth in population size and indeed the overall population for that year.For the stated question-
There are ten huge male cattle on a farm right now. In order to boost the number of animals, the farmer brings in a pregnant rabbit. The inexperienced farmer expects her rabbit population to double each month.Thus, number of animals after years;
= 10 x 2⁷
= 1280
Thus, number of animals will the farmer have after 7 months including the 10 cattle are 1280.
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tim buys a torch and a battery. the torch costs 11 times as much as the battery. tim pays with a £10 note and gets £4.84 change how much does the battery cost?
Answer:
43 p
Step-by-step explanation:
total cost = 10 - 4.84 = 10.00 - 4.84 = £5.16
b + t = 5.16
t = 11b
b + 11b = 5.16
12b = 5.16
12 / 12 b = 5.16/12
b = £0.43
PLSSSS helpp with these
1. Let f(x)=2x+7 and g(x)=3x^2+2
Find f(g(3))
590
65
5
29
2. Let f(x)=4x and g(x)=(x−2)^2
Find g(f(x))
16x^2-16x+4
16x^2-4
16x^2-12x-4
16x+4
3.Let f(x)=2x+1 and g(x)=−7x+1
Find g(f(2))
-26
20
-34
-35
Answer:
1. D 2. C 3. C
Step-by-step explanation:
On my test
ok so i did this twice but got wrong answer need help with this one rq
By solving an inequality, we will see that option a is cheaper for more than 60 miles.
For what number of miles is option A better?We know that option A charges $25 per day plus $0.15 per mile, so the cost for x miles is given by the linear equation:
A(x) = $25 + $0.15*x
While for option B the fixed cost is $10 and the cost per mile is $0.40, so the cost equation is:
B(x) = $10 + $0.40*x
The cost of option a will be smaller when:
$25 + $0.15*x < $10 + $0.40*x
$25 - $10 < $0.40*x - $0.15*x
$15 < $0.25*x
$15/$0.25 < x
60 < x
So for 60 miles the cost is the same, for x > 60 miles the cost of option a will be smaller (because the slope is smaller).
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you tossed a coin 100 times and get only 27 heads. do you have a reason to expect that the coin is unfair? explain g
Therefore, coin is unfair ,It is true that the coin can be considered unfair.
What is probability ?Calculating or estimating how likely or "possible" something is to occur is the subject of probability. Words like "certain," "impossible," or "probable" can be used to express the likelihood of an event occurring. Probabilities in mathematics are always expressed as fractions, decimals, or percent with values ranging from 0 to 1.
Here,
Step 1: We see that a coin is tossed 100 times, but we only receive heads 27 times.
In other words, the odds of a head are 27/100 or 0.27.
It is thought that there will be an equal number of heads and tails on a fair coin (or very close, if not equal).
So, using a fair coin:
P(H)=P(T)=0.5
Step 2
But in this instance, P(H)=0.27, which is a long way from 0.5.
Therefore, coin is unfair.
It is true that the coin can be considered unfair.
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Find the values of x and y.
Answer:
x = 90 , y = 43
Step-by-step explanation:
Since AB and AC are congruent , then Δ ABC is isosceles with base angles congruent , that is
∠ ABD = ∠ ACD = 47°
AD is the perpendicular bisector of BC , so
∠ ADB = x = 90
the sum of the 3 angles in Δ ABD = 180° , then
y = 180° - (90 + 47) = 180 - 137 = 43
3(4x+2)=(?)x+( )
Enter the number that goes in the green box
Or
Bill write 4 page per hour. I the total number of page written proportional to the number of hour pent writing?
Equation used to represent the relation between the number of pages written to the number of hours used with constant of proportionality is
x = 4y.
As given in the question,
Let us consider number of pages write by Bill be 'x'
And number of hours represented by 'y'
Number of hours used by Bill to write 4 pages = 1 hour
Number of pages written by Bill in 1 hour = 4
Given :
Number of pages is proportional to the number of hours
⇒ x ∝ y
⇒ x = ky
Where 'k' is the constant of proportionality.
When x = 4 , y = 1
substitute the value in the equation,
4 = k(1)
⇒ k = 4
Now the required equation with the constant of proportionality k = 4 is:
x = 4y
Therefore, the required equation to represent the relation between number of pages written to the number of hours used with constant of proportionality is equal to x =4y.
The complete question is:
Bill enjoys writing in his spare time. He writes 4 pages per hour. The proportional relationship between the number of pages written to the number of hours is represented by the equation ______. Write the equation in standard form with a constant of proportionality.
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Please HELP WITH CHEM
The ratio of Oats to Maple syrup for 36 cookies is 192 grams: 816 grams. So the answer is Option C. 192 grams: 816 grams.
What is Ratio:Comparing two amounts of the same units and determining the ratio tells how much of one quantity is in the other.
when evaluating the relationship between two quantities or numbers. In general, x: y, which can be interpreted as "x is to y," is used to denote a ratio between two quantities.
Here we have
15 Cookies need 80g Oats
=> Amount of Oats for 1 cookie = 80g/15 gms
So the amount Oats for 36 Cookies = 80g/5 × 36 = 192 grams
15 Cookies need 340 grams of Maple syrup
=> Amount of Maple syrup for 1 cookie = 340/15 gram
So the amount of Maple syrup for 36 cookies = (340/15)×36 = 816 grams
By the above calculations,
For 36 Cookies we need 192 grams of Oats and 816 grams of Maple syrup
The Ratio of Oats to Maple syrup = 192 gram: 816 gram
Therefore,
The ratio of Oats to Maple syrup for 36 cookies is 192 grams: 816 grams. So the answer is Option C. 192 grams: 816 grams.
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Which is an equation of the line through the origin and (-5, 6)?
The equation of line through the origin and (-5, 6 ) is y = [tex]-\frac{6}{5}x[/tex]
What is slope?The slope of a line is the ratio of the amount that y increases as x increases some amount. Slope tells you how steep a line is, or how much y increases as x increases. The slope is constant (the same) anywhere on the line.
the coordinates of the origin is (0, 0) and h other coordinates are (-5, 6)
at x = 0 and y = 0
using the equation of straight line y = mx + c
0 = 0(m) + c
so c = 0
at x = -5, y = 6
6 = -5m +c
but c = 0
6 = -5m
m = -6/5
Equation of line becomes y = -6/5x
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The amount of time a certain brand of light bulb lasts is normally distribued with a
mean of 1900 hours and a standard deviation of 45 hours. Out of 670 freshly installed
light bulbs in a new large building, how many would be expected to last more than
1890 hours, to the nearest whole number?
To earn a "C" in Probability, Sam must get a grade average of at least 70%.
Sam's test scores are 62, 71, and 65. His final exam score counts as 3 test
scores in the average. What is the minimum score Sam needs to get on his
final exam to get a "C" in the course?
The minimum score Sam needs to get on his final exam to get a "C" in the course is 82.
What is a probability?
A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
Given that, Sam's test scores are 62, 71, and 65.
The total score in three test is (62 + 71 + 65) = 198
Assume that, he scored x in the final test.
Total score of Sam is 198 + x.
He needs to score 70% means he needs to score 70 out of 100.
According to question,
(198 + x)/ 400 ≥ 70/100
Multiply both sides by 100:
(198 + x)/ 4 ≥ 70
Multiply both sides by 4
198 + x ≥ 280
x ≥ 280 - 198
x ≥ 82
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Step 1: we know that angle t s r is-congruent-to angle q r s because all right angles are congruent. step 2: we know that angle t is-congruent-to angle q because it is given. step 3: we know that line segment s r is-congruent-to line segment r s because of the reflexive property. step 4: triangle t s r is-congruent-to triangle q r s because of the asa congruence theorem. of the aas congruence theorem. of the third angle theorem. all right triangles are congruent.
With the help of congruency of triangles rules, we know that TSR ≅ QRS because of (B) the AAS congruence theorem.
What is the congruency of triangles?Two triangles are said to be congruent if all three corresponding sides and all three corresponding angles have the same size.
These triangles can be moved, turned, flipped, and rotated to produce the same appearance.
When moved, they are parallel to one another.
So, we have two sets of angles and one common side.
Review the congruence situations.
SSS ⇒ Three sides in the first, three sides in the second.
SAS: two sides, including the angle of the first side.
Incorporating angle in the second.
2 angles and the side that joins them in the first, according to ASA
Two angles and the side that connects the two angles.
AAS = 2 angles in the first triangle, plus 1 side.
Second, and one side in △.
Let's read the statements again and fill in the blanks.
Step 1: Since all right angles are congruent, mTSR = mQRS = 90°.
Step 2: Since it is given, mT = mQ
Step 3: Due to the reflexive property, SR becomes RS (common side)
Step 4: Because of the AAS congruence theorem, TSR and QRS are required.
Therefore, with the help of congruency of triangles rules, we know that TSR ≅ QRS because of (B) the AAS congruence theorem.
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The correct form of a question:
Given: TSR and QRS are right angles; T ≅ Q
Prove: TSR ≅ QRS
Step 1: We know that TSR ≅ QRS because all right angles are congruent.
Step 2: We know that T ≅ Q because it is given.
Step 3: We know that SR ≅ RS is because of the reflexive property.
Step 4: TSR ≅ QRS because __________
a. of the ASA congruence theorem
b. of the AAS congruence theorem
c. of the third angel theorem
d. all right triangles are congruent
Ms. patels gym class is practicing soccer. Ms. pedal has 18 soccer balls and three teams of students. She gives the same number of bars to eat student. How many balls does Ms. patel give each team
Answer
6
Step-by-step explanation:
There are 3 teams and 18 soccer balls. For each team to have the same number of soccer balls you need to do 18 divided by 3 to get 6. Each time will have 6 soccer balls.
Vince had 10 weeks to get in shape for a race. The line graph shows how many miles he ran per training session each week.
Answer:
13
Step-by-step explanation:
You take the number of miles from weeks 5-8 and add them up. 2+3+4+4=13
Question 6(Multiple Choice Worth 2 points)
(Two-Column Tables MC)
The table below shows the ratios of black to white keys on pianos of various sizes.
Black A 18 45 72
White 13 B 65 C
Determine which table has the correct values for A, B, and C.
The correct values for A, B and C are given as follows:
A = 9.B = 26.C = 104.How to obtain the correct values for A, B and C?The table shows the ratios of black to white keys on pianos of various sizes, and these ratios are constant, meaning that the following proportional relationship is established:
A/13 = 18/B = 45/65 = 72/C
Then the value of A can be obtained as follows:
A/13 = 45/65
Applying cross multiplication, we have that:
65A = 13 x 45
A = 13 x 45/65
A = 9.
The value of B can be obtained as follows:
18/B = 45/65
Applying cross multiplication, we have that:
45B = 18 x 65
B = 18 x 65/45
B = 26.
Finally, the value of C can be obtained as follows:
72/C = 45/65
Applying cross multiplication, we have that:
45C = 72 x 65
C = 72 x 65/45
C = 104.
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Help please!!!!!!!! I’m confused
Answer:
y = 0
Step-by-step explanation:
x + 2y = 2 ( subtract 2y from both sides )
x = 2 - 2y → (1)
x = - 4y + 2 → (2)
substitute x = 2 - 2y into (2)
2 - 2y = - 4y + 2 ( add 4y to both sides )
2 + 2y = 2 ( subtract 2 from both sides )
2y = 0 , then
y = 0
An engineer looks up at the top of a cell tower. The engineer stands 30 meters from the center of the tower with a line of sight of 37° from the horizontal. The engineer's eyes are 2
meters above the ground.
The value of the tangent of angle 37° is 3/4. Then the height of the cell tower will be 24.5 meters.
What is trigonometry?Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
A specialist gazes toward the highest point of a cell tower. The specialist stands 30 meters from the focal point of the pinnacle with a view of 37° from the level. The designer's eyes are 2 meters over the ground.
Let 'h' be the height of the tower. Then we have
tan 37° = (h - 2) / 30
Simplify the equation, then we have
tan 37° = (h - 2) / 30
3/4 = (h - 2) / 30
4h - 8 = 90
4h = 98
h = 24.5 meters
The level of the cell pinnacle will be 24.5 meters.
The diagram is given below.
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A large university accepts 70% of the students who apply. Of the students the university accepts, 50% actually enroll. If 10,000 students apply, how many actually enroll?
For this we have to calculate 50% of 7,000 which is 3,500
What does a math percent mean?
In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).
What is the formula for percentage?
By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.
first we have to calculate 70% of 10,000 which is 7,000
Then now we have to calculate 50% of 7,000 which is 3,500
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Solve the inequality for z.
z - 3 > 11
Simplify your answer as much as possible.
Answer: z > 14
Step-by-step explanation:
Move 3 to the right
The lines 5x + 2y = 14 and y = –5x + 9 are A. parallel b.perpendicular c.neither
Answer:
parallel
Step-by-step explanation:
same slope
How many solutions does this equation have?
-2-y=-y
no solution
one solution
infinitely many solutions
Answer:
No solution
Step-by-step explanation:
-2-y=-y
clt
-2=-y+y
-2=0
:ans is -2=0 making it with no solution
answer the question linked
Determine the equation of the ellipse with foci (-6,-1) and (-6,-7), and co-vertices (-2,-4) and (-10,-4)
The equation of ellipse with foci (-6,-1) and (-6,-7), and co-vertices (-2,-4) and (-10,-4) is [tex]\frac{(x+6)^2}{25}+\frac{(y+4)^2}{16}=1[/tex]
What is equation of an ellipse?
The standard equation of an ellipse centered at (h, k) with a major axis parallel to the x-axis is given by:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]
where the coordinates of the vertex are (h±a, 0), coordinates of co-vertex are (h, k ± b) and the coordinates of foci are (h±c, k), where a² = c² + b².
According to the given question:
Given foci of the ellipse :
(-6, -1) and (-6, -7)
Co-vertices of the ellipse :
(-2, -4) and (-10, -4)
From the given foci and vertices ,
c = -1 - (-7) /2 = 3
b = -2 - (-10) /2 = 4
c² = a² + b²
∴ a² = 3 x 3 + 4 x 4 = 25
( h, k) = (-6 - 6 /2 , -1 - 7 / 2) = (-6, -4)
Equation of the ellipse is given by:
(x - h)²/ a² + (y - k)²/b² =1
(x - (-6))²/ 25 + (y - (-4))²/16 = 1
[tex]\frac{(x+6)^2}{25}+\frac{(y+4)^2}{16}=1[/tex]
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What inequality represents the graph? 4 . -8-40 48 x <= - 8; x < - 8; x > - 8; x < 8
Option 1 : x < = - 8 represents the given graph of inequality.
What is inequality?In mathematics, an inequality displays the connection between two values in an unbalanced algebraic expression. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signs.
Depending on which way the inequality sign is pointing, a sign can be greater or less than. When the open portion of the sign is facing left, >, the value on the left side of the sign is greater than the value on the right. When it is turned to the right, the left value is less than the right value.
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