Answer:
f(x)=(2.5)x
Step-by-step explanation:
x equals the number of years after 2010, and every year after 2010 their total corn harvest increases by 2.5%, so you would have 2.5 multiplied by however many years after 2010 it is
The exponential function f(x) that models the number of bushels of corn produced x years after 2010 is f(x) = 175000(1.025)^x
How to calculate compound interest's amount?If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:
[tex]CI = P(1 +\dfrac{R}{100})^T - P[/tex]
The final amount becomes:
[tex]A = CI + P\\A = P(1 +\dfrac{R}{100})^T[/tex]
We can use compound interest formula whenever there is compounding (increment or decrement) per unit time.
Here, the initial amount of production farm was doing in 2010 is 175000 bushels of corn.
This value increases by 2.5% per year.
We need the final number of bushels of corn that will be produce x years after 2010.
So, here, we can take P = 175000, R = 2.5, and T = x
Then, we get:
[tex]f(x) = A = 175000\left(1 + \dfrac{2.5}{100}\right)^x\\\\f(x) = 175000(1.025)^x[/tex]
Thus, the exponential function f(x) that models the number of bushels of corn produced x years after 2010 is [tex]f(x) = 175000(1.025)^x[/tex]
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Part B The manager of The Gadget Factory wants to make sure that the next shipment costs no more than $15,000. Write an inequality that shows the amount of money that can be spent. Graph the inequality on the number line. Let n=the amount of money spent.
Answer:
Part B The manager of The Gadget Factory wants to make sure that the next shipment costs no more than $15,000. Write an inequality that shows the amount of money that can be spent. Graph the inequality on the number line. Let n=the amount of money spent.
Step-by-step explanation:
The inequality equation is n ≤ 15,000 , where n is the amount of money spent
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
Let the amount of money spent be represented as n
And , the next shipment costs no more than $15,000
So , n ≤ 15,000 be equation (1)
Therefore , the value of A is n ≤ 15,000 and the graph is plotted
Hence , the inequality equation is n ≤ 15,000
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Hank and Rosa play the following game: A bag has 15 tiles in it, each with a letter from the phrase probability game on it. Hank and Rosa take turns drawing a tile, recording the letter, and placing the tile back in the bag. Hank earns a point if he draws a vowel. Rosa earns a point if she draws a consonant. They decide that the letter y can be a vowel or a consonant. Which statement best explains whether or not the game is fair?
A. The game is not fair because the probability of Hank drawing a winning letter is less than the probability of Rosa drawing a winning letter.
B. The game is fair because Hank and Rosa have the same probability of drawing a winning letter.
C. The game is fair because both Hank and Rosa will get a point if the letter y is drawn.
D. The game is not fair because the probability of Hank drawing a winning letter is greater than the probability of Rosa drawing a winning letter.
Answer:
A
Step-by-step explanation:
There are 8 consonants (not including y) and only 6 vowels (not including y), so Rosa has a higher probability of winning.
The game is not fair because the probability of Hank drawing a winning letter is less than the probability of Rosa drawing a winning letter.
What is probability?
'Probability is defined as the possibility of an event to happen is equal to the ratio of the number of outcomes to the total number of outcomes.'
According to the given problem,
There are 8 consonants (not including y) and only 6 vowels (not including y), so Rosa has a higher probability of winning.
Hence, we can conclude that the game is not fair the probability of Hank drawing a winning letter is less than the probability of Rosa drawing a winning letter.
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What is the area of a circle with a radius of 4 cm? Give your answer in terms of pi.
(This is a math question from flocabulary, and I really need help!!)
Answer:
r = the radius, in your case, it's 4 cm. So. Area = π ×r2. = π× (4 cm)2. = 16π cm2 ≈ 50.24 cm2.
Step-by-step explanation:
Which of the following sets of side lengths could produce a triangle? Select
all that apply.
13 mm, 5 mm, and 6 mm
2 cm, 7 cm, and 6 cm
2 m, 5 m, and 7 m
6 ft, 6 ft, and 12 ft
The sets of side lengths that can produce a triangle are
2 cm, 7 cm, and 6 cm2 m, 5 m, and 7 m6 ft, 6 ft, and 12 ftThe triangle inequality theorem states that the sum of any two sides of a triangle is greater than or equal to the third side.
That is, in a given triangle of sides a, b and c,
a + b ≥ c
Analysing the sets of the side lengths given,
In triangle 2 cm, 7 cm, and 6 cm,
2 + 6 = 8,
Therefore 8cm which is greater than the third side being 7cm makes this side lengths possible to produce a triangle.
In triangle 2 m, 5 m, and 7 m,
2 + 5 = 7
Addition of both sides of the triangle is equal to the third side being 7m.
In triangle 6 ft, 6 ft, and 12 ft,
6 + 6 = 12
Addition of both sides of the triangle is equal to the third side being 12ft
Therefore the sets of side lengths could produce a triangle are
2 cm, 7 cm, and 6 cm
2 m, 5 m, and 7 m
6 ft, 6 ft, and 12 ft
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the sum of 2 consecutive integers is three times their difference what is the larger number
Answer:
2
Step-by-step explanation:
Let the two consecutive integers be x , x+1
Sum : x + x +1 = 2x + 1
Difference: (x +1) - 1 = x + 1 - 1 = x
Sum = 3 times their difference
2x + 1 = 3 * x
2x + 1 = 3x
1 = 3x - 2x
1 = x
The numbers are 1 , 2
If the center of a circle is at (a, b) and the radius of the circle is c, how would you write the equation of the circle?
Answer:
Step-by-step explanation:
(x-a)² + (y-b)² = c²
a bed room set is being sold for $5500 if bought cash
Answer:
$5700 - $5500= $200
Explanation:
The total installments: 24 ($175) = $4200
The hire purchase price: $1500 + $4200 = $5700
The amount saved by paying cash: $5700 - $5500= $200
ixl i need help asap
Answer:
1. Baseball
2. Soccer ball
3. Football
Explantion:
Speed = Distance / time
Baseball --> 1270/32 = 39.69
Football --> 1199/44 = 27.25
Soccer ball --> 1270/44 = 28.86
Answer:
1. Baseball
2. Soccer ball
3. Football
Formula= Speed = Distance / time
Baseball in fraction form is 1270/32 and in decimal form is 39.69
Football in fraction from is 1199/44 and in decimal form is 27.25
Soccer ball in fraction form is 1270/44 and in decimal 28.86
Hope this helps <3 Need thanks? Comment /hearthelp
I have a question on triangle congruence its a homework assignment
Explain what is a SYSTEM OF LINEAR EQUATIONS?
What is the sum of the polynomials?
(6x + 7 + X ²) + (2x² - 3)
0 -X2+6x+4
3x2 +6x+4
9x + 4
O 9x2 +4
Answer:
B) 3x^2+6x+4
Step-by-step explanation:
(6x+7+x^2)+(2x^2-3)
6x+7+x^2+2x^2-3
3x^2+6x+7-3
3x^2+6x+4
The sum of the polynomials is 3x² + 6x + 4.
What are Polynomials?Polynomials are mathematical expressions which consist of one or more terms involving variables and coefficients connected with operations like multiplication, subtraction, addition and natural number powers of variables.
Given are two polynomials whose sum has to be found.
(6x + 7 + x ²) and (2x² - 3).
The sum of the polynomials is,
(6x + 7 + x ²) + (2x² - 3)
We have to operate the like terms together.
= (6x) + (7 - 3) + (x² + 2x²)
= 6x + 4 + 3x²
= 3x² + 6x + 4
Hence the sum of the polynomials is 3x² + 6x + 4.
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Please help me on my math assignment you have to write an inequality that models the combinations of multiple choice and essay questions you could answer during the test without running out of time.
Answer:
x + 15y ≤ tStep-by-step explanation:
From the table we see that:
Each multiple choice question takes 1 min and each essay takes 15 min to complete.x multiple choice questions will take x min and y essays will take 15y minTotal time required is x + 15yIf you have t minutes to complete the test then required inequality is:
x + 15y ≤ tits the last answer thanks :)
Answer:
(7,0)
Step-by-step explanation:
Write the equation for the line in point-slope form that passes through the point (- 4, - 6) with a slope of 34
Answer:
34 minus -6 minus= -6
Step-by-step explanation:
RHOMBUS The diagonals of rhombus ABCD intersect at E. Given that
mZBAC = 53° and DE = 8, find the indicated measure.
B
А.
53°
mZAED
m2 DAC
m ZADC
AE
DB
8
E
с
AC
D
11. Name the four isosceles triangles in rhombus ABCD.
12. Name three properties of AC and BD.
Answer:
Question 11:
[tex]\angle DAC = 53^\circ[/tex]
[tex]\angle AED = 90^\circ[/tex]
[tex]\angle ADC = 74[/tex]
[tex]DB = 16[/tex]
[tex]AE = 6.03[/tex]
[tex]AC = 12.06[/tex]
Question 12:
[tex]\triangle ABD[/tex], [tex]\triangle BAC[/tex], [tex]\triangle CDA[/tex] and [tex]\triangle DAB[/tex]
Question 13:
AC and BD are perpendicular lines, and they are diagonals
Step-by-step explanation:
Question 11
Given
[tex]\angle BAC = 53^\circ[/tex]
[tex]DE = 8[/tex]
See attachment for Rhombus
Required
Determine the indicated sides
Solving (a): [tex]\angle DAC[/tex]
Diagonal CA divides [tex]\angle DAB[/tex] into 2 equal angles
i.e
[tex]\angle DAC = \angle BAC[/tex]
So:
[tex]\angle DAC = 53^\circ[/tex]
Solving (b): [tex]\angle AED[/tex]
The angles at E is 90 degrees because diagonals AC and BD meet at a perpendicular.
So:
[tex]\angle AED = 90^\circ[/tex]
Solving (c): [tex]\angle ADC[/tex]
First, we calculate [tex]\angle ADE[/tex], considering [tex]\triangle ADE[/tex]:
[tex]\angle ADE + \angle AED + \angle DAC = 180[/tex]
[tex]\angle ADE + 90 + 53 = 180[/tex]
[tex]\angle ADE + 143 = 180[/tex]
[tex]\angle ADE = -143 + 180[/tex]
[tex]\angle ADE = 37[/tex]
To calculate [tex]\angle ADC[/tex], we have:
[tex]\angle ADC = 2*\angle ADE[/tex]
[tex]\angle ADC = 2* 37[/tex]
[tex]\angle ADC = 74[/tex]
Solving (d): [tex]DB[/tex]
From the rhombus
[tex]DB = DE +EB[/tex]
Where
[tex]DE =EB[/tex]
So:
[tex]DB = 8 + 8[/tex]
[tex]DB = 16[/tex]
Solving (e): [tex]AE[/tex]
To do this we consider [tex]\triangle ADE[/tex]
Using the tan formula
[tex]tan(\angle ADE) = \frac{AE}{DE}[/tex]
[tex]\angle ADE = 37[/tex] and [tex]DE = 8[/tex]
So:
[tex]\tan(37) = \frac{AE}{8}[/tex]
[tex]AE = 8 * \tan(37)[/tex]
[tex]AE = 6.03[/tex]
Solving (f): [tex]AC[/tex]
This is calculated as:
[tex]AC = AE + EC[/tex]
Where
[tex]AE = EC[/tex]
[tex]AC = 6.03 +6.03[/tex]
[tex]AC = 12.06[/tex]
Question 12: Isosceles Triangle
In the rhombus, all 4 sides are equal;
So, the isosceles triangle are:
[tex]\triangle ABD[/tex], [tex]\triangle BAC[/tex], [tex]\triangle CDA[/tex] and [tex]\triangle DAB[/tex]
Question 13:
AC and BD are perpendicular lines, and they are diagonals
y=3(50)x
Based on the previous problem, how many bacteria will there be in 8 hours?
A. 74
B. 6,611
C. 1,200
D. 328, 050
Answer:
y=3(50)×
y=3(50) 8
50×3=150
150×8=1,200
Need help in math will give brain if right
Answer:
c)
Step-by-step explanation:
What is the arc length of an arc with radius 14 in and central angle 66^o? Show all calculations that lead to the answer and include units.
Answer:
28pi*66/360
Step-by-step explanation
Used the equation Central angle/360*2pi r
you roll a die twice. What is the probability of rolling a 3 and then a 4?
Answer:
1/36
Step-by-step explanation:
P(rolling a 3) and P(rolling a 4)
= 1/6 and 1/6
=(1/6)(1/6)
=1/36
Find the measures of angle A, B, C and D.
Answer: b = 48 c = 26 d = 106 a = 26
Step-by-step explanation:
find the value of given expression
[tex] \sqrt{9 \times 81 \times 9} [/tex]
Answer:
√{9×81×9}=√(9²×9²)=±(9×9)=±81
Answer:
your answer will be 81
Step-by-step explanation:
.......
Winnie when she fell asleep sitting up so she just kept going back lol now I’m on a rampage posting my cats :,)
Answer:
that's an adorable little baby.
Step-by-step explanation:
Answer:
its cute
Step-by-step explanation:
(-15)-(-18) divided by 3
Answer:
The answer is (-9)
Step-by-step explanation:
The solution is, the result of the division is 1.
What is division?Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
given that,
(-15)-(-18)
now we have to divide this by 3
so, we get,
(-15)-(-18) /3
now,
(-15)-(-18)
= -15 + 18
=3
so, we have,
(-15)-(-18) /3
=3 /3
=1
Hence. The solution is, the result of the division is 1.
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are these triangles congruent ?
Answer:
yes
Step-by-step explanation:
from sss axiom
we can say that they are congurqnt
Which of the following statements must be true based on the diagram below? Answer correctly !!!!!!!! Will mark brainliest !!!!!!!!!!!!
Answer:
3rd one
Step-by-step explanation:
JAERA HAD 13 TOY CARS. SHE BOUGHT 26 CARS FROM THE TOY STORE AND GOT 23 FOR HER BDAY. JAERA GAVE 10 CARS TO HER CAITLYN SHAW AND 38 TO HER COUSIN. HOW MANY TOY CARS DOES SHE HAVE LEFT?
What is the interest rate if…
Principal = $1,250
Time = 4 years
Interest = $285.
840 Km in 12 hours.Whatis the average speed.
Help me please thanks
Replace x any with the given values:
x/y = 9/3 = 3
The answer is 3
Are the fractions 3/8 and 9/27 equivalent? If yes, explain how you know they are equivalent. If they are not equivalent, what is a fraction that would be equivalent to 3/8.
Answer:
Step-by-step explanation:
The factors are 9 and 27 are 1,3,9,27
With that, 9/27 is undoubtedly reducible to 1/3
Before now,we were told that when a number divides itself,the result is zero...now,⅜÷⅓ should give us 1 but 3/8×3/1 = 9/8 and 9/8≠1 hence,they aren't same!