Mathematics is a branch of science that deals with numbers, quantities and shapes. It includes arithmetic, geometric, algebra, calculus and many more. It also refers to the study of relationship between numbers or items.
One example is counting numbers which we are using almost everyday in our life.
1, 2, 3, 4 and so on.
The population of an endangered species of fish living in a controlled habitat is given by the equation P = 7t + 46, where Pis the population and t is the time in months since the population was introduced into the habitat. Graph the equation using t = 0, 6, 12, and 18. (100 pts)
Graph is attached. It will be a linearly increasing line.
Population for 0 months is 46
Population for 6 months is 88
Population for 12 months is 130
Population for 18 months is 172.
Given,
The equation for population, P = 7t + 46
P is the population
t is the time in months
We have to graph the equation using
t = 0, 6, 12 and 18.
For this we have to find P
1. t = 0
P = 7t + 46 = 7 × 0 + 46 = 0 + 46 = 46
2. t = 6
P = 7t + 46 = 7 × 6 + 46 = 42 + 46 = 88
3. t = 12
P = 7t + 46 = 7 × 12 + 46 = 84 + 46 = 130
4. t = 18
P = 7t + 46 = 7 × 18 + 46 = 126 + 46 = 172
The graph is given below and it will be a linearly increasing line.
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the following group of equations represents which type of system {x^2 + y^2 = 9 x^2/16 + y^2/9 =1
The given group of equations represents a system of non-linear equations.
How to know if an equation is linear or nonlinear?A mathematical equation must take the form y = m x +b in order to be classified as a linear function (in which m is the slope and b is the y-intercept). This form cannot be satisfied by a nonlinear function.
Only first degree variables and terms that contain the products of variables are present in a linear equation.
However, in the case of nonlinear equations, either the equation comprises a product of variables or at least one of the variables is not of the first degree.
If the graph of an equation is a straight line, the equation is linear. Otherwise, if the power of x is more than one, then it is nonlinear.
The given equations has the degree more than 1 and their graph is also not a straight line.
Hence, the given group of equations represents a system of non-linear equations.
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What ever I'm doing is making the circle equal 410 degrees.
Step 1
Redraw the cyclic quadrilateral
From the image;
[tex]\begin{gathered} mSTU=220 \\ \text{mSRU}=360\text{ -220=110(sum of angles at a point or in a circle is 3}60^o) \end{gathered}[/tex]Step 2
Find the measure of angle R
[tex]m\angle R=\frac{1}{2}mSTU[/tex][tex]m\angle R=\frac{1}{2}\times220=110[/tex]Find the measure of angle T
[tex]\begin{gathered} m\angle T=\frac{1}{2}mSRU \\ m\angle T=\frac{1}{2}\times140 \\ m\angle T=70 \end{gathered}[/tex]Find the measure of angle U
[tex]m\angle U=360-95-110-70=85\text{ ( sum of angles in quadrilateral)}[/tex]Find the measure of Arc SRU
[tex]\begin{gathered} \text{mSRU}=\text{ }360-\text{mSTU} \\ \text{mSRU}=360-220=140 \end{gathered}[/tex]Find the measure of Arc mRUT
[tex]\begin{gathered} \text{mRUT}=\text{ 2}\times m\angle S \\ \text{mRUT}=2\times95=190 \end{gathered}[/tex]Find the measure of mRST
[tex]\begin{gathered} \text{mRST}=2\times m\angle U \\ \text{mRST}=2\times85=170 \end{gathered}[/tex]the model of the skateboard you want to buy is available in 9 different colors and 3 different styles. in how many ways can you order the board?
Multiply the number of colors by the number of styles
9 x 3 =27 ways
Give two real-world situations that could be represented by the value -2
We have to represent two real world situations that could be represented by the value -2.
(1) Let there be a fish which is 2 meter below the sea level.
Considering the sea level point to be zero and denoting the points above sea level as positive and the points below sea level as negative, like we do in a cartesian plane, the point which is 2 meter below the ground level will be -2.
(2) Let there be a box buried 2 feet under the ground.
Considering the ground level to be zero and denoting the point above the ground level as positive and the points below ground level as negative, the point which is 2 meter below the ground level will be -2.
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Every hour on the hour, Helen does jumping jacks. At 4:00 she does 4 jumping jacks. At 5:00 she does 5 jumping jacks, etc. How many jumping jacks will Helen do, in total, from the time prior to her final jumping jacks at 4:00 to the time prior to her first jumping jacks at 11:00 ?a) 46b) 56c) 57d) 60
We have to add the jumping jacks from 4:00 (not included) to 11:00.
So we have to add:
[tex]\sum ^{11}_{n\mathop=5}n=5+6+7+8+9+10+11=56[/tex]The answer is option b) 56.
What is the slope of the line passing through (5, 0) and (2, 0)
A) 2/5
B) 0
C) 5/2
D) Undefined
For the square ABCD, it is known that | AB| = | AC| and |DA| = |DC| and corner ABC =
corner CDA. One of the corners of this square is 150 degrees. Find the sizes of the three remaining angles of the square ABCD.
Answer:
∠BAD = 150°∠ABC = 48°∠BCD = 114°∠ADC = 48°Step-by-step explanation:
Given quadrilateral ABCD with AB≅AC, DA≅DC, ∠ABC≅∠ADC, and one of the corner angles equal to 150°, you want the measures of all corner angles.
SetupThe given congruent angles and sides are marked in the attached diagram. If we let ∠ACB = x and ∠ACD = y, we can write some equations involving the sums of the various angles.
First of all, we note that both triangles are isosceles. That means ...
∠ABC≅∠ACB = x∠DAC≅∠DCA = yThe sum of angles in ∆ACD must be 180°, so we have ...
x + 2y = 180°
We know that the isosceles triangle base angles cannot exceed 90°, so the angles at corners B and D cannot be 150°. That leaves two possibilities:
(a) Corner angle C is 150° ⇒ x + y = 150°
(b) Corner angle A is 150° ⇒ (180°-2x) +y = 150°
Solution(a) Corner C is 150°
This makes the system of equations for x and y be ...
x +2y = 180°x +y = 150°Subtracting the second from the first gives y = 30°, and substituting that value for y gives x = 120°. We already know x is the base angle of an isosceles triangle, so cannot have that value. This possibility is eliminated.
(b) Corner D is 150°
This makes the system of equations for x and y be ...
x +2y = 180°(180° -2x) +y = 150°The second of these equations can be rearranged to ...
2x -y = 30°
Adding twice this to the first equation, we have ...
2(2x -y) +(x +2y) = 2(30°) +(180°)
5x = 240°
x = 48°
Substituting for x in the second equation gives ...
2(48°) -y = 30°
96° -30° = y = 66°
As we noted in the solution part (a), corner angle C is the sum of x and y:
∠BCD = x +y = 48° +66° = 114°
Corner anglesThen the corner angles are ...
∠BAD = 150°∠ABC = 48°∠BCD = 114°∠ADC = 48°The attached figure is drawn to scale.
If cos(theta) = 5/0 and is in the 1st quadrant, find the following:
step 1
Find out sine
Remember the identity
[tex]cos^2\theta+sin^2\theta=1[/tex]substitute the given value of cosine
[tex]\begin{gathered} (\frac{5}{9})^2+s\imaginaryI n^2\theta=1 \\ \\ s\imaginaryI n^2\theta=1-\frac{25}{81} \\ \\ s\mathrm{i}n^2\theta=\frac{56}{81} \\ \\ sin\theta=\frac{\sqrt{56}}{9} \\ \\ sin\theta=\frac{2\sqrt{14}}{9} \end{gathered}[/tex]step 2
Find out cosecant
[tex]\begin{gathered} csc\theta=\frac{1}{sin\theta} \\ \\ csc\theta=\frac{9}{2\sqrt{14}}*\frac{\sqrt{14}}{\sqrt{14}}=\frac{9\sqrt{14}}{28} \\ \\ csc\theta=\frac{9\sqrt{14}}{28} \end{gathered}[/tex]step 3
Find out secant
[tex]\begin{gathered} sec\theta=\frac{1}{cos\theta} \\ \\ sec\theta=\frac{9}{5} \end{gathered}[/tex]step 4
Find out tangent
[tex]\begin{gathered} tan\theta=\frac{sin\theta}{cos\theta} \\ \\ tan\theta=\frac{\frac{2\sqrt{14}}{9}}{\frac{5}{9}}=\frac{2\sqrt{14}}{5} \end{gathered}[/tex]step 5
Find out cotangent
[tex]\begin{gathered} cot\theta=\frac{1}{tan\theta} \\ \\ cot\theta=\frac{5}{2\sqrt{14}}*\frac{\sqrt{14}}{\sqrt{14}}=\frac{5\sqrt{14}}{28} \\ \\ cot\theta=\frac{5\sqrt{14}}{28} \end{gathered}[/tex]The graph of F(x), shown below, resembles the graph of G(x) = x², but it hasbeen changed somewhat. Which of the following could be the equation ofF(x)?OA Fx)=0.3x²+2 OB. F(x)=3x2+2OC. F(x) = -x²2² +2D. F(x)=x²+2
Answer:
Explanation:
Given the function:
[tex]G(x)=x^2[/tex]The graph of G(x) is wider than the graph of F(x), so we can conclude that G(x) has been stretched vertically by a factor greater than 1 to obtain F(x).
Furthermore, G(x) was translated upwards by 2 units when we compare the vertices.
Thus, from the options,a possible equation for F(x) is:
[tex][/tex]Answer:F(x)=3x^2+2
Step-by-step explanation:
suppse that you buy and exerice ball with diameter of 85 cm and your brother buys and exercise ball with 65 cm what is the diffrence bewtween the volume and surface are of both balls? round to the nearest 100
Given:
• Diameter of my ball = 85 cm
• Diameter of my brother's ball = 65 cm
Let's find the difference between the volume of the both balls and also let's find the difference between the surface area of both balls.
A ball has the shape of a sphere.
Therefore, we have the following formulas:
• Volume of a sphere formula:
[tex]V=\frac{\pi d^3}{6}[/tex]• Surface area of a sphere formula:
[tex]A=\pi d^2[/tex]Where d is the diameter.
• Now, to find the difference between the volume of both balls, we have:
[tex]V_1=\frac{\pi d^3}{6}=\frac{\pi85^3}{6}=321555.09\approx321555\text{ cm}^3[/tex]The volume of my ball is 321555 cubic cm.
[tex]V_2=\frac{\pi *65^3}{6}=143793.3\approx143793\text{ cm}^3[/tex]Volume of my brother's ball is 143793 cubic cm.
Therefore, to find the difference between the volume of both balls, we have:
V = V1 - V2 = 321555 - 143793 = 177762 cm³ = 177800 cm³
The difference between the volume of both balls is 177800 cm³
• Now for the surface area, we have:
[tex]A_1=\pi d^2=\pi *85^2=22698.01=22698\text{ cm}^2[/tex]The surface area of my ball is 22698 cm²
For surface area of my brother's ball:
[tex]A_2=\pi d^2=\pi *65^2=13273.23\approx13273\text{ cm}^2[/tex]The surface area of my brother's ball is 13273 cm².
Difference of surface areas:
A = A1 - A2 = 22698 - 13273 = 9425 cm² = 9400 cm²
Therefore, the difference between the surface area of both balls is 940O cm².
ANSWER:
• Difference between volume of both balls= 177800 cm³
• Difference between the surface area of both balls = 9400 cm²
Nancy is buying a new pair of boots. The store is having a sale and all boots are 20% off. Part A Choose an expression that can represent the sale price of the boots where x is the original price of the boots (0.2x, 0.8x, 1.2x) Part B Thus means that the sale price of the boots is (20%, 80%, 120%) of the original. cost
Answer:
Part A: 0.8x
Part B: 80% of the original price.
Explanation:
Part A:
The store sells the boots at a sale price of 20% off, meaning the price of the shoes is 100% - 20 % = 80% of the original price. If we call x the original price, then the sale price would be
[tex]\frac{80}{100}\times x[/tex][tex]=0.8x[/tex]Part B:
The sale price of the boots is 100% - 20% = 80% of the original price.
Hannah's friend Ami would like the group of 5 performers to include more.
males than females. The order in which they perform is no longer
relevant.
iii) Find the number of different selections of 5 performers with more
males than females.
iv) Two of the applicants areMr andMrs Blake. Find the number of
different selections that include Mr and Mrs Blake and also fulfil Ami's.
requirement.
Answer:
iii) 501
iv) 110
Step-by-step explanation:
See picture
Which equation in standard form has a graph that passes through the point (2,19) and has a slope of 11/2
Answer:
y=5.5x+8
Step-by-step explanation:
Replace x and y values so you get 19=5.5(2)+cMultiply 5.5 by 2 to get 19=11+cSubtract 11 from both sides to get 8=cSimplify to y=5.5x+8Can some on help me on these please and thank you!
at 3:00 am the temperature was -8 degrees.By early evening, the temperature rose 25 degrees at late day the temperature dropped 5 degrees. What was the late day temperature?
According to the problem:
• At 3:00 am the temperature was -8°.
,• Then, it rose 25 degrees. ,This implies a sum.
,• At last, it dropped 5 degrees. ,This implies a subtraction.
Remember that "rising" shows a positive direction and "dropping" shows a negative direction. Following this rule, we can form the following expression
[tex]T=-8+25-5[/tex]There you can observe that the initial temperature (-8) increased (+)25, and then decreased (-)5.
Therefore, the temperature for the late day is
[tex]T=12[/tex]Multiply.3/5⋅3/4Enter your answer as a fraction in simplest form in the box.
Hello!
We have the following multiplication:
[tex]\frac{3}{5}\times\frac{3}{4}[/tex]To solve it, we have to multiply numerator with numerator and denominator with denominator, look:
[tex]\frac{3}{5}\times\frac{3}{4}=\frac{3\times3}{5\times4}=\frac{9}{20}[/tex]So, the fraction in is the simplest form is 9/20.
3/5 3) Find the equation of the line passing through the points (1, -2) and (-2, 7). Write the equation in slop-intercept from. Oy = 3x - 5 Oy= 3x + 13 Oy=-3x + 1 Oy=-3x - 2 Previous Next Submit arch O
hello
to solve this question we would first of all find the slope of the line
[tex]\begin{gathered} slope(m)=\frac{y_2-y_1}{x_2-x_1} \\ \end{gathered}[/tex][tex]\begin{gathered} y_1=-2 \\ x_1=1 \\ y_2=7 \\ x_2=-2 \end{gathered}[/tex]we can now substitute this into the equation
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{7-(-2)}{-2-1} \\ m=\frac{7+2}{-3}=\frac{9}{-3}=-3 \end{gathered}[/tex]the slope of the line is -3
we can write out how the equation looks
[tex]\begin{gathered} y=mx+b \\ y=-3x+b \\ b=\text{intercept} \end{gathered}[/tex]we can use one of the points to solve for b
[tex]\begin{gathered} y=-3x+b \\ u\sin g\text{ the first point} \\ (1,-2) \\ -2=-3(1)+b \\ -2=-3+b \\ b=3-2 \\ b=1 \end{gathered}[/tex]we can now rewrite our equation with slope and intercept
[tex]\begin{gathered} y=mx+b \\ y=-3x+1 \end{gathered}[/tex]from the calculation above, the equation of the line is given as y = -3x + 1
372.2 is what percent of 642
Answer:
57.97507788%
Step-by-step explanation:
Write the problem as a mathematical expression.
372.2
642
Multiply by 100 to convert to a percentage.
372.2
642 * 100
Simplify
372.2.
642. * 100 = 57.97507788%
20 more than half a number is 70 what is the number
i need help can anyone help me please??
Hence the second option, [tex]y=\frac{2}{3}x +\frac{11}{3}[/tex] is the correct option.
What is slope interception form?
Y=mx+b, where m is the slope and b is the y-intercept, is the slope intercept form. The graph of the linear equation can be drawn on the x-y coordinate plane using this form of the equation.
For the given question we are given,
slope (m) = 2/3
and we are also given the point that the line passes through to be,
(-1,3).
that is
(x,y)=(-1,3)
x=-1
y=3
we, know that slope interception form is of the form,
y=mx+c
substituting the value of m (slope) and the point (-1,3) we get
3=(2/3)*(-1)+b
= 3= -2/3 +b
= 3+2/3=b
= (9+2)/3=b
= 11/3=b
from this we get b=11/3
now substituting this again in
y=mx+b
we get
y=(2/3)x+(11/3)
Hence the second option [tex]y=\frac{2}{3}x +\frac{11}{3}[/tex] is correct.
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what is the answer to 7 3/16 + 4 5/48
Answer:
[tex]11\frac{14}{48}[/tex]
Step-by-step explanation:
[tex]7\frac{3}{16}+4\frac{5}{48}[/tex]
First, make these improper fractions.
[tex]\frac{115}{16} +\frac{197}{48}[/tex]
And now to add these fractions, make the denominators the same.
For that, multiply both the numerator and denominator of the fraction 115/16 by 3.
[tex]\frac{115*3}{16*3} +\frac{197}{48}\\\\\frac{345}{48} +\frac{197}{48}\\\\\frac{542}{48} \\\\=11\frac{14}{48}[/tex]
Write a math problem that this expression could be used to represent. Create a visual fraction model to represent the situation. Record the equation with the product. 9x6
Please, give me some minutes to take over your question
Ben run 6 miles in an hour. How many miles does Ben run in nine hours?
Ratio
6 miles / 1 hour
6 miles/ 1 hour = x miles / 9 hours
x= 6 * 9 = 54 miles
Ben runs 54 miles in 9 hours.
Dose anyone get this i am confused
Answers:
a) 32500
b) 0.00604
c) 2.4 * 10^6
d) 1.47 * 10^(-3)
===================================================
Explanation:
The exponent over the 10 tells us how many spaces to move right or left. If the exponent is positive, we move right. If negative, we move left. Think of a number line.
For part (a), the exponent is 4. So we move the decimal point 4 spaces to the right.
The 3.25 then becomes 32500
--------------
In part (b), the exponent -3 means we move 3 spots to the left to go from 6.04 to 0.00604
---------------
Part (c)
Place the decimal point between the first two digits and erase the zeros to get 2.4
Then we need to move the decimal point 6 spots to the right to get back to 2,400,000 again
Therefore we can say 2,400,000 = 2.4*10^6
---------------
Part (d)
Place the decimal point just after the first nonzero digit, and erase the zeros to the left to get 1.47
We must move the decimal point 3 spots to the left to go from 1.47 back to 0.00147 again
It means 0.00147 = 1.47*10^(-3)
Answer: he is right
Step-by-step explanation:
A random sample of 269 student were asked what kind of vehicle they prefer a car truck the following contingency table gives the 2 way classification of the responses
Given a random sample of 269 students and a contigency table that gives the 2 way classification of their responses.
The probability formula is:
[tex]P(E)=\frac{n(\text{Required outcome)}}{n(\text{Possible outcome)}}[/tex][tex]P(\text{Female)}=\frac{(99+22)}{269}=\frac{121}{269}=0.450[/tex][tex]P(\text{Car)}=\frac{(87+99)}{269}=\frac{186}{269}=0.691[/tex][tex]\begin{gathered} P(\text{Female}|\text{Truck)}=\frac{P(\text{Female }\cap\text{ Truck)}}{P(\text{Truck)}} \\ =\frac{22}{(61+22)}=\frac{22}{83}=0.265 \end{gathered}[/tex][tex]P(\text{Truck }\cap\text{ Female)=}\frac{22}{(99+22)}=\frac{22}{121}=0.182[/tex]The conditional probability P(A/B) or P(B/A) arises only in the case of dependent events.
please follow directions and refer to rubric Will mark brainliest
screenshots attached thank you I really need this
Answer:
Step-by-step explanation: To find the x-intercept, substitute in
0
for
y
and solve for
x
. To find the y-intercept, substitute in 0 for x
and solve for y
x-intercept(s): 735,0
y-intercept(s): 0,490
Given f(x)=-2x-1f(x)=−2x−1, solve for x when f(x)=-7f(x)=−7
The value of the function f(x) = 2x -1 when f(x) = 7 is 13.
Function:
A function is defined as a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given,
Here we have the function f(x) = 2x - 1.
Now, we need to find the value of the function when f(7).
To find the value of f(7), we have to replace the value of x with the value 7.
Then we get the equation like the following,
f(7) = 2(7) - 1
Now, we have to expand the terms in order to solve it,
f(7) = 14 - 1
When we subtract it, then we get the value of
f(7) = 13.
Therefore, the value of f(7) = 13.
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complete it for me please urgent
Answer:
8. y=3x+2
9. y=2x-6
10. y=1/2x+3
14. y=-2x
all i know hope this helps
I need help with this question but no one is helping me! Can someone please help me.
Step-by-step explanation:
"with replacement" is important.
that means that the mixture of the marbles and therefore the chances to pull certain marbles does not change with the previous pull.
a probability is always
desired cases / totally possible cases
we have 14 marbles in the bag
4 orange
2 green
8 purple
the probability to pull an orange marble is therefore
4/14 = 2/7
the probability to pull a green marble is therefore
2/14 = 1/7
the probability to pull a purple marble is therefore
8/14 = 4/7
a.
a green marble is pulled AND then a purple marble is selected.
we need to combine both probabilities for one combined event :
1/7 × 4/7 = 4/49
b.
a purple marble and then a green marble is selected.
4/7 × 1/7 = 4/49
since we replace the marbles after every pull, both probabilities are the same, of course.
every pull has the same probability for each desired event.
c.
2 orange marbles are selected.
2/7 × 2/7 = 4/49
d.
2 non-orange marbles are pulled
there are 10 non-orange marbles. so this is
10/14 × 10/14 = 5/7 × 5/7 = 25/49
How many times greater is the value of 4,563 than the value of 4.563?
The given number 4,563 is 4558.437 times greater than 4.563.
What is decimal?
Decimals are numbers that have two components, a whole number component and a fractional component, which are separated by a decimal point. 12.5 is a decimal number, for instance.
Using a single notation, decimals can convey both the entire number and the fraction. Whole numbers and fractions are separated from each other in decimals by a point called a decimal point. For instance, in the number 65.4, the entire number is 65, while the fractional half is 4 (10).
The given numbers are 4,563 that is four thousand five hundred sixty- three and 4.563 that is four point five six three.
The difference between these two numbers is 4558.437.
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