Solution
Step-by-step explanation:
Given:-
- The population in year 1987, Po = 5 billion
- Growth rate, r = 1.4%
World population follows an exponential growth model
Find:-
The projected world population in 2017.
Solution:-
- The exponential growth model is mathematically expressed as:
Population in x year = Po* ( 1 + r/100)^( x - xo )
Where, xo: The base year.
- Plug in the values and solve for the projected population in year 2017:
Population in 2017 year = 5,000,000,000* ( 1 + 1.4/100)^( 2017 - 1987 )
Population in 2017 year = 5,000,000,000* ( 1 + 0.014)^( 30 )
[tex]\begin{gathered} =5000000000(1.014)^{30} \\ =16216987550.1377 \end{gathered}[/tex]Therefore the projected world population = 16,216,987,550.1 (1d.p)
graph the equation y= -1
This equation takes the value of -1 for all values of x in the plane. So that,
COLOR THEME O ZOOM 11. Larry purchased 0.4 pounds of jellybeans for his niece. If the jellybeans cost 70¢ per pound, which model represents how to determine the amount Larry paid for the jellybeans? < PREVIOUS 7 8 9
We know that
• He purchases 0.4 pounds of jelly beans.
,• Each pound costs 70 cents.
To determine the amount of money Larry paid, we can use the following proportion.
[tex]\frac{0.70}{1}=\frac{x}{0.4}[/tex]Then, we solve for x.
[tex]x=0.70\cdot0.4=0.28[/tex]Larry paid 28 cents for 0.4 pounds of jelly beans for his niece.Given the table values, Determine the base for the expoent function
To determine the value of the exponential function:
[tex]y=a^x[/tex]we use the first values from the table and plug them in the expression for the function:
[tex]\begin{gathered} \frac{1}{81}=a^{-\frac{1}{2}} \\ \frac{1}{a^2}=\frac{1}{81} \\ a^2=81 \\ a=\sqrt[]{81} \\ a=9 \end{gathered}[/tex]Therefore the base of the exponent function is 9
What is the solution to the equation below? Round your answer to two decimal places.3x = 9.2A.x = 2.02B.x = 2.22C.x = 0.50D.x = 0.96
A)2.02
ExplanationStep 1
given
[tex]3^x=9.2[/tex]a) write the rigth side of the equation as a fraction
[tex]9.2=\frac{92}{10}=\frac{46}{5}[/tex]hence
[tex]3^x=\frac{46}{5}[/tex]b) take the logarithms in both sides
[tex]\begin{gathered} 3^x=\frac{46}{5} \\ \ln3^x=ln\frac{46}{5} \\ apply\text{ the property} \\ x=log_3(\frac{46}{5}) \\ x=2.02 \end{gathered}[/tex]so, the answer is
A)2.02
If M is between G and T, MG = 5x+3, MT = 2x-1, and GT = 37then x = MG =MT =
We have:
Then:
[tex]\begin{gathered} MG+MT=GT \\ 5x+3+2x-1=37 \end{gathered}[/tex]And solve for x:
[tex]\begin{gathered} 7x+2=37 \\ 7x+2-2=37-2 \\ 7x=35 \\ \frac{7x}{7}=\frac{35}{7} \\ x=5 \end{gathered}[/tex]Therefore, for MG and MT:
[tex]\begin{gathered} MG=5(5)+3=25+3=28 \\ MT=2(5)-1=10-1=9 \end{gathered}[/tex]Answer:
x = 5
MG = 28
MT = 9
Sarah is conducting a science experiment the directions tell her to mix 5 parts of substance B how many mililters of substance A should she use
Answer: She should use 25 millimeters of substance A
This is a case of ratio. Substance A and B are to be mixed in a given ratio such that as A increases, B would similarly increase, not by the same quantity but by the same ratio. That means every time you add 5 parts of A, you need to add 3 parts of B. In effect, if you add 5 parts of A ten times (5 * 10 = 50 parts) you will need to add 3 parts of B ten times also (3 * 10 = 30).
So the
The average score on a stats midterm was 73 points with a standard deviation of 7 points. Gregory s-score was -2. How many points did he score?
scoressolution
average = 73
SD = 7
then
[tex]-2=\frac{n-73}{7}[/tex]where n = number of points, so:
[tex]\begin{gathered} -2\cdot7=\frac{n-73}{7}\cdot7 \\ -14=n-73 \\ -14+73=n-73+73 \\ n=59 \end{gathered}[/tex]answer: 59 points he scores
What is the area of the trapezoid? 5 km G 4 km km 9 km 21 square kilometers
We can calculate the area of the trapezoid by multiplying the height and the average of the top and bottom parallel sides.
The height is always measured perpendicularly to the parallel sides, as is shown in the picture.
Then, we can calculate the area as:
[tex]\begin{gathered} A=(\frac{a+b}{2})\cdot h \\ A=(\frac{5+9}{2})\cdot3 \\ A=\frac{14}{2}\cdot3 \\ A=7\cdot3 \\ A=21\operatorname{km}^2 \end{gathered}[/tex]Answer: the area is 21 km^2.
Given that GEO - FUN, Snd UF12 ft17 ftE15 ftUFEft
Since this is a congruent triangle problem, The side UF is equal to side GE
so UF is 12
The definition of congruent triangles is "Two triangles are congruent if they have the same shape and the same size"
Solve the system with elimination.3x + y = 9x + 2y = 3
In order to solve by elimination, let's multiply the first equation by -2. This way, when we add the equations, the variable y will be canceled out:
[tex]\begin{cases}-6x-2y=-18 \\ x+2y={3}\end{cases}[/tex]Now, adding the equations, we have:
[tex]\begin{gathered} -6x-2y+x+2y=-18+3\\ \\ -5x=-15\\ \\ x=\frac{-15}{-5}\\ \\ x=3 \end{gathered}[/tex]Now, calculating the value of y, we have:
[tex]\begin{gathered} x+2y=3\\ \\ 3+2y=3\\ \\ 2y=0\\ \\ y=0 \end{gathered}[/tex]Therefore the solution is (3, 0).
what is the value?[tex]8 + 4x \geqslant 12[/tex]
Given the equation:
[tex]8\text{ }+\text{ 4x }\ge\text{ 12}[/tex]We are required to find x.
First subtract 8 from both sides:
[tex]8\text{ - 8 }+\text{ 4x }\ge\text{ 12 -8}[/tex][tex]4x\text{ }\ge\text{ 4}[/tex]Now, divide both sides by 4
[tex]\frac{4x}{4}\text{ }\ge\text{ }\frac{4}{4}[/tex][tex]x\text{ }\ge\text{ 1}[/tex]We did not flip the inequality sign because we divided both sides by a posite number and not a negative number. The inequality sign should be flipped only when both sides are divided by a negative number.
Hello there I need help with this question please make it simple I am in year 9
Use the substitution method to solve the system of equations.
Let k be the cost of a knife and s be the cost of a spoon.
Since a knife is four times the cost of a spoon, then:
[tex]k=4s[/tex]Since 12 spoons and 16 knives cost 105.64, then:
[tex]12s+16k=105.64[/tex]Replace the expression for k in terms of s into the second equation:
[tex]12s+16(4s)=105.64[/tex]We obtained an equation in a single variable. Solve for s:
[tex]\begin{gathered} \Rightarrow12s+64s=105.64 \\ \Rightarrow76s=105.64 \\ \Rightarrow s=\frac{105.64}{76} \\ \therefore s=1.39 \end{gathered}[/tex]Replace the value of s into the expression for k to find the cost of a knife:
[tex]\begin{gathered} k=4s \\ \Rightarrow k=4(1.39) \\ \therefore k=5.56 \end{gathered}[/tex]Therefore, the cost of one knife is equal to £5.56.
What is the formula for converting a quadratic formula to standard form?
we have that
the quadratic formula is of the form
Ax^2+Bx+C=0 ------> that is the standard form of the quadratic equation
A quadratic equation can be written in vertex form
so
y=a(x-h)^2+k
where
(h,k) is the vertex of the quadratic equation
a is the leading coefficient
To convert vertex form to the standard equation
step 1
y=a(x-h)^2+k
y=a(x^2-2hx+h^2)+k
y=ax^2-2ahx+ah^2+k
group terms
y=ax^2-2ahx+(ah^2+k)
equate to zero
ax^2-2ahx+(ah^2+k)=0
where
the coefficients A, B and C are
A=aB=-2ahC=ah^2+ktherefore
To convert a quadratic equation in vertex form to standard form, apply the formula above
The fuel efficiency ( in miles per gallon) of a car going at a speed of x miles per hour is given by the polynomial - 1/150x^2 + 1/3x. Find the fuel efficiency when x= 30 mph
Given:
The expression of fuel is given as,
[tex]f(x)=\frac{1}{150}x^2+\frac{1}{3}x\text{ . . . . . (1)}[/tex]The objective is to find the efficiency when x = 30mph.
Explanation:
To obtain the efficiency, substitute x=30 in equation (1).
[tex]f(30)=\frac{1}{150}(30)^2+\frac{1}{3}\times30[/tex]On further solving the above equation,
[tex]\begin{gathered} f(30)=\frac{900}{150}+10 \\ =6+10 \\ =16 \end{gathered}[/tex]Hence, the fu
Given that DE¯¯¯¯¯¯¯¯, DF¯¯¯¯¯¯¯¯, and EF¯¯¯¯¯¯¯¯ are midsegments of △ABC, and DE=3.2 feet, EF=4 feet, and DF=2.4 feet, what is the perimeter of △AB
Given: The triangle ABC is provided with DE = 3.2 feet, EF = 4 feet and DF = 2.4 feet.
To find: The perimeter of the triangle ABC.
Explanation:
The triangle ABC is given where DE , EF and DF are the midsegments of the triangle ABC.
If DE is the midsegment then using midsegment theorem we have
[tex]\begin{gathered} DE=\frac{1}{2}BC \\ BC=2DE \\ BC=2\times3.2 \\ BC=6.4 \\ \end{gathered}[/tex]Since, EF is the midsegment then using midsegment theorem we have
[tex]\begin{gathered} EF=\frac{1}{2}AB \\ AB=2EF \\ AB=2\times4 \\ AB=8 \end{gathered}[/tex]Since, DF is the midsegment then using midsegment theorem we have
[tex]\begin{gathered} DF=\frac{1}{2}AC \\ AC=2DF \\ AC=2\times2.4 \\ AC=4.8 \end{gathered}[/tex]We have the sides of the triangle as AB = 8 feet, BC = 6.4 feet and AC = 4.8 feet.
The perimeter of the triangle ABC will be :
P = AB+BC+AC
=8+6.4+4.8
=19.2
Therefore, the perimeter of the triangle is P = 19.2 feet
Final Answer: The perimeter is P = 19.2 feet.
y Quinn had 3 more than two times the number of marbles Rowan has. Together they have 77marbles How many marbles door each child have?
Explanation
Step 1
Let
convert words into math terms
Let
x= number of marbles Quinn has
y= number of marbles Rowan has
Quinn had 3 more than two times the number of marbles, in other words you have to add 3 to twice the number or marlbles
x=2y+3
Rowan has. Together they have 77
x+y=77
Need help with question 7 section a b and c please
We have the function h(n) = 4x+3
h(n) = 15
4x+3 = 15
4x = 12
x= 3
And f(x) = 2(4)^x
f(3) = 2(4)³
f(3) = 2*64
f(3)= 128
Write the trigonometric form of the complex number. (Let 0 ≤ < 2.)
Find: the graph of -7i
Explanation:
Final answer: option d is correct option.
Determine if the two triangles shown are similar if so right similarities statement
Let us compare the ratios of the lengths to see if there is a relationship
[tex]\begin{gathered} \frac{14}{49}=\frac{2}{7} \\ \text{also} \\ \frac{8}{28}=\frac{2}{7} \end{gathered}[/tex]From the comparison, we can see that
[tex]\frac{14}{49}=\frac{8}{28}[/tex]Then it followed that
[tex]\frac{VM}{MU}=\frac{ML}{MT}=\frac{VL}{UT}[/tex]Since the ratios of the sides of the two triangles are equals to each other, it is definite that the two triangles are similar.
Hence, triangle VLM is congruent of similar to triangle UTM
Haley practiced her free throws at the basket ball court and shot 25 times. She made 11 of her shots. What percent of her shots did she NOT make?
WE know that
• She threw 25 times.
,• She made 11 of them.
To know the percentage number that 11 presents, we just have to divide
[tex]\frac{11}{25}=0.44[/tex]Then, we multiply by 100 to express it in percentage
[tex]\text{0}.44\cdot100=44[/tex]Therefore, Haley made 44% of the shots.d. What percentage of people preferred ranch? e. What percentage of people preferred Italian or Thousand Island? f. If 200people responded to the survey, how many people preferred ranch? g. If 300people responded to the survey, how many people preferred Thousand Island. ?
Answer:
Explanation:
a) The most preferred salad dressing is the one with the highest percentage on the pie chart
That is the Ran
d) We want to get the percentage that preferred ranch
From the piechart, we can see that 55% of the people preferred ranch
e) The percentage we are talking about in this question takes two portions of the pie chart
Hence, we will add the percentages of Italian and Thousand Island
Mathematically, we have the sum as 32 + 13 = 45 %
f) From the piechart, 55% of respondents preferred ranch
This is equivalent to:
[tex]\frac{55}{100}\times200\text{ = 110 people}[/tex]g) We use the approach we applied in the last question
We have this as 13% of 300
This is equivalent to:
[tex]\frac{13}{100}\times300\text{ = 39 people}[/tex]Some of the first n terms of the geometric sequence
1) We have to find the sum of the first four terms of the geometric sequence:
[tex]3+3(\frac{1}{4})+3(\frac{1}{4})^2+3(\frac{1}{3})^3+3(\frac{1}{4})^4[/tex]In this case, we can take out the factor 3 and we have a common ratio r = 1/4. We have to add the first 5 terms.
Then, the sum can be expressed as:
[tex]S_n=\frac{a_1(1-r^n)}{1-r}[/tex]For this problem, r1 = 3, r = 1/4 and n = 5:
[tex]\begin{gathered} S_5=\frac{3(1-(\frac{1}{4})^5)}{1-\frac{1}{4}} \\ S_5=\frac{3(1-\frac{1}{1024}_)}{\frac{3}{4}} \\ S_5=\frac{3(\frac{1024-1}{1024})}{\frac{3}{4}} \\ S_5=\frac{4}{3}\cdot3\cdot\frac{1023}{1024} \\ S_5=\frac{1023}{256} \end{gathered}[/tex]2) We have this sum already solved but we can check it as:
[tex]\begin{gathered} S=\sum_{i\mathop{=}1}^7(-3)^i \\ S=(-3)+(-3)^2+(-3)^3+(-3)^4+(-3)^5+(-3)^6+(-3)^7 \\ S=-3+9-27+81-243+729-2187 \\ S=-1641 \end{gathered}[/tex]Answer:
1) 1023/256
2) -1641
In nursing one procedure for determining the dosage for a child ischild dosageage of child in yearsage of child+12- adult dosageIf the adult dosage of a drug is 328 ml., how much should a 10-year old child receive? Round your answer to the nearest hundredth.
Given:
[tex]child\text{ dosage=}\frac{age\text{ of child in year }}{\text{age of child}+12}\times adult\text{ dosage}[/tex]To determine: Child dosage given that
[tex]\begin{gathered} \text{age of chld = 10,} \\ \text{adult dosage = 328ml} \end{gathered}[/tex]Solution:
In other to determine the child dosage, we would substitute the age of the child given and the adult dosage into the formula
[tex]\begin{gathered} child\text{ dosage=}\frac{age\text{ of child in year }}{\text{age of child}+12}\times adult\text{ dosage} \\ child\text{ dosage=}\frac{10}{10+12}\times328ml \\ child\text{ dosage=}\frac{10}{22}\times328ml \end{gathered}[/tex][tex]\begin{gathered} child\text{ dosage=}\frac{3280ml}{22} \\ child\text{ dosage=}149.090909ml \\ child\text{ dosage=}149.09ml(\text{nearest hundredth)} \end{gathered}[/tex]Hence, a 10-year old child would receive to the nearest hundredth 149.09 ml
Kara categorized her spending for this month into four categories: Rent, Food, Fun, and Other. The amounts she spent in each category are pictured here.Food - 422Other - 633Rent - 528Fun - 317What percent of her total spending did she spend on Rent?Round your answer to the nearest whole percent
Kate organized her spending month in four categories:
Food - 422
Other - 633
Rent - 528
Fun - 317
The amount of the total spending is the sum of all the categories:
So 422+633+528+317 = 1900 total spending
If we want to know the percent that she spent on rent, use
Rent/total of spending
528/1900= 0.2778
Rounded to the nearest whole percent:
0.2778 = 27,78% = 28%
ned help with a question
Answer
Check Explanation
Explanation
There are two ways to evaluate this. The two methods are related too.
First method is just to use a calculator. This is the easier method.
√37 = 6.083, hence, √37 is between 6 and 7.
√2 = 1.414, hence, √2 is between 1 and 2.
√350 = 18.708, hence, √350 is between 18 and 19.
√500 = 22.361, hence, √500 is between 22 and 23.
√60 = 7.746, hence, √60 is between 7 and 8.
The second method is to note the closest perfect squares to these numbers. One wouldn't need a calculator for this.
Note that a perfect square is a number that has a whole number square root, that is, a number, whose square root is whole number.
√230
230 is bounded on both sides by the perfect squares 225 and 256.
225 = 15²
256 = 16²
So, √230 is between 15 and 16.
√190
190 is bounded on both sides by the perfect squares 169 and 196.
169 = 13²
196 = 14²
So, √190 is between 13 and 14.
√5
5 is bounded on both sides by the perfect squares 4 and 9.
4 = 2²
9 = 3²
So, √5 is between 2 and 3.
√115
115 is bounded on both sides by the perfect squares 100 and 121.
100 = 10²
121 = 11²
So, √115 is between 10 and 11.
√90
90 is bounded on both sides by the perfect square 81 and 100.
81 = 9²
100 = 10²
So, √90 is between 9 and 10.
Hope this Helps!!!
f(x) = 3x^2 - 7x + 23 for x = -2.
Given the function:
[tex]f(x)=3x^2-7x+23[/tex]Let's solve for f(x) when x = -2.
To find f(x) when x = -2, substitute -2 for x in the equation and evaluate.
Thus, we have:
[tex]\begin{gathered} f(x)=3x^2-7x+23 \\ \\ f(-2)=3(-2)^2-7(-2)+23 \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} f(-2)=3(4)-7(-2)+23 \\ \\ f(2)=12-(-14)+23 \\ \\ f(2)=12+14+23 \\ \\ f(2)=49 \end{gathered}[/tex]ANSWER:
49
1/6 of loop around the circle would be a rotation of how many degrees (q)? A=6B=60C=30D=36
Note that a whole circle measures 360 degrees.
1/6 of it will be :
[tex]\frac{1}{6}\times360^{\circ}=60^{\circ}[/tex]The answer is B. 60
quadrilateral mnop is similar to quadrilateral s r u t which proportion can be used to find the value of x
The answer is option B
Jeff is a popcorn vendor at the Linc. He is paid $50.00 for a game, plus $1.50 for each box of popcorn sold (X). If at the end of the night, he has made $182.00, how many boxed os popcorn did he sell?
evaluate -(3^-5)(3^3)
Explanation
remember how to operate exponents
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