Step 1
State the formula for the area of a trapezoid
[tex]\begin{gathered} The\text{ area of a trapezoid=(}\frac{a+b}{2})\times height(h) \\ \text{Where a= base 1=4}m \\ b=\text{base 2=12m} \\ \text{The area of the trapezoid=40m}^2 \end{gathered}[/tex]Step 2
Find the height
[tex]\begin{gathered} 40=(\frac{4+12}{2})\times h \\ 40=\frac{16}{2}\times h \\ 80=16h \\ h=\frac{80}{16} \\ h=5m \end{gathered}[/tex]Hence, the height = 5m
Isotope: 239Pu
Half-life
(years): 24,100
Initial
Quantity:
Amount After
4000 Years:
3.7g
The mass of isotope 239-Pu left after 4000 years is approximately 3.3g
RadioactivityRadioactivity is the phenomenon of the spontaneous disintegration of unstable atomic nuclei to atomic nuclei to form more energetically stable atomic nuclei. Radioactive decay is a highly exoergic, statistically random, first-order process that occurs with a small amount of mass being converted to energy.
In solving the disintegration constant, we can use the half-life formula.
The half-life of a sample is given as;
[tex]T_\frac{1}{2} = \frac{ln2}{\lambda}[/tex]
Substituting the values into the equation;
[tex]T_\frac{1}{2} = \frac{ln2}{\lambda}\\24100 = \frac{ln2}{\lambda} \\\lambda = \frac{ln2}{24100} \\\lambda = 0.00002876years^-^1[/tex]
The formula of radioactivity is given as
[tex]N = N_oe^(^-^\lambda ^t)[/tex]
No = 3.7gt = 4000We can plug in the values and solve.
[tex]N = N_oe^(^-^\lambda ^t)\\N = 3.7e^-^(^0^.^0^0^0^0^2^8^7^6 ^*^4^0^0^0^)\\N = 3.297g\\N = 3.3g[/tex]
The amount left after 4000 years is 3.3g.
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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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Write the system of equations associated with the given augmented matrix. Do not solve
The elements in the first 3 columns are the coefficients of system of equations.
The 4th column are the constants of the system of equations.
This is a system of 3 equations.
Let's write the system using the variables x, y, and z. Shown below:
[tex]\begin{gathered} 1x+1y+0z=3 \\ 0x+4y+1z=-5 \\ 1x+0y-1z=4 \end{gathered}[/tex]Let's simplify and write the equations:
[tex]\begin{gathered} x+y=3 \\ 4y+z=-5 \\ x-z=4 \end{gathered}[/tex]calculate the measure of SR
In the given figure
There is a triangle RST
∵ RU is perpendicular on ST and bisects it
∴ Triangle RST is an isosceles triangle
∴ RS = RT
∵ RS = 3x + 9 and RT = 7x + 17
Equate them
∵ 7x + 17 = 3x + 9
Subtract 3x from both sides
∴ 7x - 3x + 17 = 3x - 3x + 9
∴ 4x + 17 = 9
Subtract 17 from both sides
∵ 4x + 17 - 17 = 9 - 17
∴ 4x = -8
Divide both sides by 4 to find x
∴ x = -2
Now substitute x by -2 in the expression of RS to find its length
∵ RS = 3(-2) + 9
∴ RS = -6 + 9
∴ RS = 3
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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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]Estimate.45.86 + 54.14A.90B.99C.100D.110
We need to estimate the sum:
[tex]45.86+54.14[/tex]In order to do so, we first round each term to the nearest integer. Then we add them.
We have:
[tex]\begin{gathered} 45.86\cong46\text{ (because 0.86>0.50)} \\ \\ 54.14\cong54\text{ (because 0.14<0.50)} \end{gathered}[/tex]Then, we can estimate the sum to be:
[tex]45.86+54.14\cong46+54=100[/tex]Therefore, option C is correct.
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
Chewbacca is standing from atop a plateau 500 feet in the air looking down ata Jedi Trainee. If the Jedi Trainee is 150 feet away from the base of theplateau, what is the angle of depression from Chewbacca to the Jedi Trainee ifChewbacca's eye height is 7.25 feet?Show your work here and explain how you arrive at your answer.
In the given situation the angle of depression is θ. To find it, use the trigonometric ratio of tangent of angle θ in a right triangle (the ratio of tangent is the relation between the two legs of a right traingle):
[tex]\tan \theta=\frac{opposite\text{ leg}}{adjacent\text{ leg}}[/tex]In the given situation the opposite leg to the angle of depresion is the distance between the base of the plateau and the Jedi Trainee and the adjacent leg is the sum of 500ft in the air and Chewbacca's eye height:
[tex]\begin{gathered} \tan \theta=\frac{150ft}{500ft+7.25ft} \\ \\ \tan \theta=\frac{150}{507.25} \\ \\ \tan ^{-1}(\tan \theta)=\tan ^{-1}(\frac{150}{507.25}) \\ \\ \theta=\tan ^{-1}(\frac{150}{507.25}) \\ \\ \theta\approx16.47 \end{gathered}[/tex]Then, the angle of depression from Chewbacca to the Jedi Trainee is approximately 16.47°You have $12 left to spend. Here are your options: $12 for 6 goodie bags for your guests or $12 for 4 goodie bags for your guests. We want to get the most for what our money can buy. Show your work in the space below. Which is the better deal?
For the first deal we get 6 goodie bags for $12, let's find how much each goodie bag cost in this case by dividing $12 by 6:
[tex]\frac{12}{6}=2[/tex]In the first deal, each goodie bag costs $2.
For the second deal, we get 4 goodie bags for $12, let's also find how much is 1 goodie bag in the scenario:
[tex]\frac{12}{4}=3[/tex]In the second deal, each goodie bag costs $3.
The better deal is the first one because each goodie bag is cheaper than in the second deal.
Answer: $12 for 6 goodie bags is the better deal
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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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:
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.
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
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
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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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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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 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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20 more than half a number is 70 what is the number
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]What is the slope of the line passing through (5, 0) and (2, 0)
A) 2/5
B) 0
C) 5/2
D) Undefined
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
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+8Every 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.
Find the solution set to each inequality 6m + 2 < 5m - 4-3(x-7) > -278(p-6) - 4(p-4)
The inequality to solve is,
[tex]8(p-6)>4(p-4)[/tex]We will use the distributive property (shown below) to simplify the expression. Then, we will use algebra rules to solve the inequality.
Distributive Property
[tex]a(b-c)=ab-ac[/tex]The simplification process >>>
[tex]\begin{gathered} 8(p-6)>4(p-4) \\ 8(p)-8(6)>4(p)-4(4) \\ 8p-48>4p-16 \\ 8p-4p>-16+48 \\ 4p>32 \\ \frac{4p}{4}>\frac{32}{4} \\ p>8 \end{gathered}[/tex]Answerp > 8Multiply.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.
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.
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%
what is the value of 10-¹
The value of
[tex]10^{-1}[/tex]which can be written as:
[tex]\frac{1}{10}[/tex]is
[tex]0.1[/tex]