The length of the line segment from a to b is 6.08 units or [tex]\sqrt{37}[/tex] units.
What is the length of a line segment and what is the role of coordinates?The length is described as the distance between the two points in a line. The coordinate usually refers to the dimensions of the point with respect to the two dimension graph.
Relation between the coordinates and length: [tex]\sqrt{(x_{1} -x_{2}) ^{2} +(y_{1} -y_{2} )^{2} }[/tex]
Now let point a be ([tex]x_{1},y_{1}[/tex]) and point b be ([tex]x_{2},y_{2}[/tex])
Thus putting values,
length = [tex]\sqrt{(3-(-3))^{2}+(4-3)^{2} }[/tex]
length = [tex]\sqrt{36+1}[/tex]
length = [tex]\sqrt{37}[/tex]
Hence the length of ab is [tex]\sqrt{37}[/tex] or 6.08 units.
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If the 10 letters are {aa,aa,aa,aa,bb,bb,cc,cc RR,RR} are available and all 10 of them are to be selected without replacement,what is the number of different permutations?
In order to calculate the number of permutations, first we start with the factorial of the number of letters.
There are 10 letters, so we start with the factorial of 10.
Then, we need to check the number of repetitions. Each repetition will be a factorial in the denominator:
[tex]x=\frac{10!}{a!\cdot b!\operatorname{\cdot}...}[/tex]We have four repetitions of aa, two repetitions of bb, two repetitions of cc and two repetitions of RR, therefore the final expression for the number of permutations is:
[tex]x=\frac{10!}{4!2!2!2!}[/tex]Calculating this expression, we have:
[tex]x=\frac{10\operatorname{\cdot}9\operatorname{\cdot}8\operatorname{\cdot}7\operatorname{\cdot}6\operatorname{\cdot}5\operatorname{\cdot}4!}{4!\operatorname{\cdot}2\operatorname{\cdot}2\operatorname{\cdot}2}=\frac{10\operatorname{\cdot}9\operatorname{\cdot}8\operatorname{\cdot}7\operatorname{\cdot}6\operatorname{\cdot}5}{8}=18900[/tex]Therefore there are 18900 permutations.
cabrinha run 3/10 mile each day for 6 days how many miles did she run in off
3/10 mile per day for 6 days.
To find how many miles did she run multiply the miles per day by 6days:
[tex]\frac{3\text{mile}}{10\text{day}}\cdot6\text{days}=\frac{18}{10}\text{mile}=\frac{9}{5}\text{mile}[/tex]Then, in 6 days she run 9/5 mileEach coordinate grid shows the graph of a system of two equations. Which graph represents a system of equations with no solution? Select all that apply.
System of Linear Equations with No Solutions
A system has no solutions if two equations are parallel.
Therefore, The answer would be option:
Figure A is a scale image of Figure B.27Figure AFigure B4535What is the value of x?
Answer:
x = 21
Explanation:
Figure A is a scaled version of figure B. This means that the ratio between any two sides must be the same for both figures.
It follows then
[tex]\frac{27}{45}=\frac{x}{35}[/tex]which just means that the ratio f sides 27 with 45 must be the same as the ratio between side x and 35. Why? Because these two sides are the same across the two figures and therefore their size with respect to each other must not change.
Now to find the value of x, we simply need to solve for x.
We do this by multipying both sides by 35:
[tex]undefined[/tex]Earth's Moon is 384,400 km from Earth. What is the correct way to write this distance in scientific notation? O A. 3.844 x 105 km OB. 38.44 x 10-4 km O C. 38.44 x 104 km O D. 3.844 x 10-5 km SUBMIT
To do this, move the decimal in such a way that there is a non-zero digit to the left of the decimal point. The number of decimal places you shift will be the exponent by 10. If the decimal is shifted to the right the exponent will be negative. If the decimal is shifted to the left, the exponent will be positive.
So, in this case, you have
Therefore, the correct way to write this distance in scientific notation is
[tex]3.844\times10^5[/tex]And the correct answer is
[tex]undefined[/tex]8+7t=22 in verbal sentence
Eight plus Seven times t equals twenty-two
Explanation
Step 1
Let
a number= t
seven times a number= 7t
the sum of eigth and seven times a number=8+7t
the sum of eigth and seven times a number equals twenty-two=8+7t=22
or,in other words
Eight plus Seven times t equals twenty-two
I hope this helps you
A storage box has a volume of 56 cubic inches. The base of the box is 4 inches by 4 inches. Lin’s teacher uses the box to store her set of cubes with an edge length of 1/2 inch.If the box is completely full how many cubes are in the set?
To answer this question, we have to find the volume of one of the cubes from Lin's set. To do it use the formula to find the volume of a cube, which is the edgelength raised to 3:
[tex]\begin{gathered} V=ed^{3^{}} \\ V=(\frac{1}{2})^3 \\ V=\frac{1}{8} \end{gathered}[/tex]In this case, each cube has a volume of 1/8 cubic inches. To find the number of cubes in the set, perform the division of the volume of the box by the volume of one cube:
[tex]n=\frac{V_{box}}{V_{cube}}=\frac{56}{\frac{1}{8}}=8\cdot56=448[/tex]The set has 448 cubes.
Scientists are conducting an experiment with a gas in a sealed container. The mass of the gas is measured and the scientists realize that the gas is leaking over time in a linear way. Eight minutes since the experiment started the gas had a mass of 302.4 grams. Seventeen minutes since the experiment started the gas had a mass of 226.8 gramsLet x be the number of minutes that have passed since the experiment started and let y be the mass of the gas in grams at that moment. Use a linear equation to model the weight of the gas over time.a) This lines slope-intercept equation is [ ] b) 39 minutes after the experiment started, there would be [ ] grams of gas left. c) if a linear model continues to be accurate, [ ] minutes since the experiment started all gas in the container will be gone.
Here, we want to model an experiment linearlly
From the question, we have it that;
The coordinates are written as;
(number of minutes, mass of gas)
So, what we have to do know is to set up the two given points
These are the points;
(8,302.4) and (17,226.8)
Now, using these two points, we can model the equation
We start by getting the slope of the line that passes through these two points
To do this, we shall use the slope equation
We have this as;
[tex]\begin{gathered} \text{slope m = }\frac{y_2-y_1}{x_2-x_1} \\ \\ (x_1,y_1)\text{ = (8,302.4)} \\ (x_2,y_2)\text{ = (17,226.8)} \\ \text{substituting these values;} \\ m\text{ = }\frac{226.8-302.4}{17-8}\text{ = }\frac{-75.6}{9}\text{ = -8.4} \end{gathered}[/tex]The general equation representing a linear model is ;
[tex]\begin{gathered} y\text{ = mx + b} \\ m\text{ is slope} \\ b\text{ is y-intercept} \\ y\text{ = -8.4x + b} \end{gathered}[/tex]To get the y-intercept so as to write the complete equation, we use any of the two points and substitute its coordinates
Let us substitute the coordinates of the first point
[tex]\begin{gathered} 302.4\text{ = -8.4(8) + b} \\ 302.4\text{ = -67.2 + b} \\ b\text{ = 67.2 + 302.4} \\ b\text{ = 369.6 } \end{gathered}[/tex]a) Thus, we have the complete linear model as;
[tex]y\text{ = -8.4x + 369.6}[/tex]b) To get this, we simply substitute the value of x given into the linear model
[tex]\begin{gathered} y\text{ = -8.4(39) + 369.6} \\ y\text{ = -327.6 + 369.6} \\ y\text{ = 42} \end{gathered}[/tex]39 minutes after the experiment started, there would be 42 grams
c) If all the gas is gone, then the value of y will br zero at this point
To get the corresponding x-value which is the time, we have it that;
[tex]\begin{gathered} 0\text{ = -8.4x +369.6} \\ 8.4x=\text{ 369.6} \\ x\text{ = }\frac{369.6}{8.4} \\ x\text{ = 44} \end{gathered}[/tex]In 44 minutes, all the gas in the container will be gone
In the triangle below, if B = 69°, A = 32°, c = 5.7, use the Law of Sines to find a. Round your answer to the nearest hundredth.
We know that the interior angles have to add to 180°, then we have that:
[tex]\begin{gathered} C=180-69-32 \\ C=79 \end{gathered}[/tex]Hence angle C=79°.
Now that we know the angle C we can use the law of sines to find a; the law of sines states that:
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]From this we have the equation:
[tex]\frac{\sin A}{a}=\frac{\sin C}{c}[/tex]Plugging the values given and solving for a we have:
[tex]\begin{gathered} \frac{\sin32}{a}=\frac{\sin 79}{5.7} \\ a=(5.7)\frac{\sin 32}{\sin 79} \\ a=3.08 \end{gathered}[/tex]Therefore a=3.08
is this equation no solution, one solution, or infinitely may solutions
Given:
[tex]\begin{gathered} x+4y=8\ldots\ldots\ldots\ldots(1) \\ y=-\frac{1}{4}x+2\ldots\ldots\ldots\ldots(2) \end{gathered}[/tex]To solve for x and y:
Substitute the equation (2) in (1) we get,
[tex]\begin{gathered} x+4(-\frac{1}{4}x+2)=8 \\ x-x+8=8 \\ 8=8 \end{gathered}[/tex]Therefore, the given system has infinitely many solutions.
the pie chart below shows how the annual budget for general Manufacturers Incorporated is divided by department. use this chart to answer the questions
You can read a pie chart as follows
Looking at the given pie chart.
The budget for Research is arounf 1/6
The budget for Engineering is around 2/6
The budget for Support is around 1/8
The budget for media and marketing are 1/16 each
The budget for sales is around 3/16
a) The department that has one eight of the budget is Support.
b) The budgets for sales and marketing together add up to
[tex]\frac{3}{16}+\frac{1}{16}=\frac{4}{16}=\frac{1}{4}[/tex]Multiply it by 100 to express it as a percentage
[tex]\frac{1}{4}\cdot100=25[/tex]25% of the budget correpsonds to sales and marketing
c) The budget for media looks around one third the budget for research, to determine the percentage of budget that corresponds to media, divide the budget of research by 3
[tex]\frac{18}{3}=6[/tex]The budget for media is 6%
Eliana drove her car 81 km and used 9 liters of fuel. She wants to know how many kilometres she can drive on 22 liters of fuel. She assumes her car will continue consuming fuel at the same rate. How far can Eliana drive on 22 liters of fuel? What if Eliana plans to drive from Dubai to Abu Dhabi via Sheikh Zayed Bin Sultan which is 139.4 km? How many liters of fuel does she need?
Eliana can drive 198 km with 22 liters of fuel.
If Eliana plans to drive from Dubai to Abu Dhabi via Sheikh Zayed Bin Sultan which is 139.4 km then she would need 15.5 liters of fuel
In this question, we have been given Eliana drove her car 81 km and used 9 liters of fuel.
81 km=9 liters
9 km= 1 liter
She wants to know the distance she can drive on 22 liters of fuel. She assumes her car will continue consuming fuel at the same rate.
By unitary method,
22 liters = 22 × 9 km
= 198 km
Also, given that if Eliana plans to drive from Dubai to Abu Dhabi via Sheikh Zayed Bin Sultan which is 139.4 km.
We need to find the amount of fuel she would need.
Let 139.4 km = x liters
By unitary method,
x = 139.4 / 9
x = 15.5 liters
Therefore, Eliana can drive 198 km with 22 liters of fuel.
If Eliana plans to drive from Dubai to Abu Dhabi via Sheikh Zayed Bin Sultan which is 139.4 km then she would need 15.5 liters of fuel
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find the values of x and y that maximize the objective function c = 3x + 4y for the graph
Answer: The correct answer is x=0 and y=4 or (0,4) per the graph
Step-by-step explanation:
To find the maximum value, we must test each point using the equation:
Check for (0,4):
C=3x+4y
C=3(0)+4(4)
C=16
Check for (2,2):
C=3(2)+4(2)
C=6+8
C=14
Check for (4,0):
C=3(4)+4(0)
C=12
Answer:
Step-by-step explanation:
Which lines are parallel?
M: y + 1 = -3 (x-1)
K: y =3(x+2)
P: y + 4 = 3x
The most appropriate choice for equation of line in slope intercept form will be given by-
line K is parallel to line P
line M is not parallel to both line K and line P.
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx +c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line
For M
y + 1 = -3(x - 1)
y + 1 = -3x + 3
y = -3x + 3-1
y = -3x + 2
Slope of M = -3
For K
y = 3(x+2)
y = 3x + 6
Slope of K = 3
For P
y + 4 = 3x
y = 3x - 4
slope of P = 3
Since Slope of K = Slope of P,
line K is parallel to line P
Since slope of M is different from slope of both K and P,
line M is not parallel to both line K and line P.
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The number of microbes in a tissue sample is given by the functionN (t) = 34.8 + In(1 + 1.2t)where N(t) is the number of microbes (in thousands) in the sample after thours.a.) How many microbes are present initially?b.) How fast are the microbes increasing after 10 hours?
Explanation
[tex]N(t)=34.8+\ln (1+1.2t)[/tex]we have a function where the number of microbes ( N) depends on the time(t)
hence
Step 1
a.) How many microbes are present initially?
to know this, we need replace time I= t = zero, because it was "initially"
so
when t=0
replace.
[tex]\begin{gathered} N(t)=34.8+\ln (1+1.2t) \\ N(0)=34.8+\ln (1+1.2\cdot0) \\ N(0)=34.8+\ln (1) \\ N(0)=34.8+0 \\ N(0)=34.8 \end{gathered}[/tex]so, initially there were 34.8 microbes
Step 2
b)How fast are the microbes increasing after 10 hours?
to know this, let t=10
so
[tex]\begin{gathered} N(t)=34.8+\ln (1+1.2t) \\ N(10)=34.8+\ln (1+1.2\cdot10) \\ N(10)=34.8+\ln (1+12) \\ N(10)=34.8+\ln (13) \\ N(10)=34.8+2.56 \\ N(10)=37.36 \end{gathered}[/tex]therefore , after 10 hours the number of microbes is 37.36
I hope this helps you
A child has an empty box that measures 4 inches by 6 inches by 3 inches. View the figure.What is the length of the longest pencil that will fit into the box, given that the length of the pencil must be a whole number of inches? Do not round until your final answer.
Solution
For this case we can do the following:
We can find the value of s on this way:
[tex]s=\sqrt[]{6^2+4^2}=\sqrt[]{52}=7.21[/tex]And solving for r we got:
[tex]r=\sqrt[]{6^2+3^2}=\sqrt[]{45}=6.71[/tex]Then the answer for this case would be:
[tex]\sqrt[]{52}=7.21[/tex]which describes the solution of the inequality y>-15? a) solid vertical line through (0,-15) with shading to the left of the line. b) dashed vertical line through (0,-15) with shading to the left of line. c) solid horizontal line through (0,-15) with shaing below line. d) dashed horizontal line through (0,-15) with shaing above line.
The solution to the inequality y > - 15 is all values of y greater than -15. This means the number -15 itself is not included; therefore, the line is a dashed line that passes through (0, -15). Furthermore, the > sign implies that the shaded region is found above the dashed line. Hence, the solution to our inequality is a dashed horizontal line through (0, -15), with shading above the line.
The first three terms of a sequence are given. Round to the nearest thousandth (ifnecessary).15, 18, 108/5. find the 8th term
SOLUTION
The following is a geometric series
We will use the formula
[tex]T_n=ar^{n-1}[/tex]Where Tn is the nth term of the series,
n is the number of terms = 8,
a is the first term = 15
And r is the common ratio = 1.2 (to find r, divide the second term, 18 by the first term which is 15
Now let's solve
[tex]\begin{gathered} T_n=ar^{n-1} \\ T_8=15\times1.2^{8-1} \\ T_8=15\times1.2^7 \\ T_8=15\times3.583 \\ T_8=53.748 \end{gathered}[/tex]So the 8th term = 53.748
4. Driving on the highway, you can safely drive 65 miles per hour. How far can you drive in ‘h’ hours? What is the domain of the function which defines this situation?A) 65B) the number of hours you driveC) the distance you driveD)the amount of gas you use
Answer:
[tex]\text{ The number of hours you drive.}[/tex]Step-by-step explanation:
For distance, we can apply the following equation:
[tex]\begin{gathered} d=s*h \\ where, \\ s=\text{ speed} \\ h=\text{ hours} \end{gathered}[/tex]Since we know that we can safely drive 65 miles per hour, the domain will be defined by the number of hours you drive:
[tex]d=65h[/tex]Answer the questions below about the quadratic function.g(×)=2×^2-12×+19Does the function have a minimum or maximum? minimum or maximum what is the functions minimum or maximum value?Where does the minimum or maximum value occur?x=?
Given the function:
[tex]g(x)=2x^2-12x+19[/tex]Let's determine if the function has a minimum or maximum.
The minimum and maximum of a function are the smallest and largest value of a function in a given range or domain
The given function has a minimum.
Apply the general equation of a quadratic function:
[tex]y=ax^2+bx+c[/tex]To find the minimum value, apply the formula:
[tex]x=-\frac{b}{2a}[/tex]Where:
b = -12
a = 2
Thus, we have:
[tex]\begin{gathered} x=-\frac{-12}{2(2)} \\ \\ x=-\frac{-12}{4} \\ \\ x=3 \end{gathered}[/tex]To find the function's minimum value, find f(3).
Substitute 3 for x in the function and evaluate:
[tex]\begin{gathered} f(x)=2x^2-12x+19 \\ \\ f(3)=2(3)^2-12(3)+19 \\ \\ f(3)=2(9)-36+19 \\ \\ f(3)=18-36+19 \\ \\ f(3)=1 \end{gathered}[/tex]Therefore, the function's minimum value is 1
Therefore, the functions minimum value occurs at:
x = 3
ANSWER:
• The function has a minimum
• Minimum value: 1
• The minimum occurs at: x = 3
PLEASE ITS URGENT I NEED HELP!!! I BEG YOU GUYS PLEEAASEEE THANKS..
Explanation
remember some properties of the exponents
[tex]\begin{gathered} a^m\cdot a^n=a^{m+n} \\ (a^m)^n=a^{m\cdot n} \\ a^{-m}=\frac{1}{a^m} \end{gathered}[/tex]then, to solve this solve each option and compare
Step 1
[tex]6^{-5}\cdot6^2[/tex]solve
[tex]\begin{gathered} 6^{-5}\cdot6^2=6^{-5+2}=6^{-3} \\ \end{gathered}[/tex]so, this is not an answer
Step 2
[tex](\frac{1}{6^2})^5[/tex]solve
[tex]\begin{gathered} (\frac{1}{6^2})^5=(6^{-2})^5=6^{(-2\cdot5)}=6^{-10} \\ \end{gathered}[/tex]so, this is an answer
Step 3
[tex]\begin{gathered} (6^{-5})^2 \\ \text{solve} \\ (6^{-5})^2=6^{-5\cdot2}=6^{-10} \end{gathered}[/tex]so, this is an answer
Step 4
[tex]\begin{gathered} \frac{6^{-3}}{6^7} \\ \text{solve} \\ \frac{6^{-3}}{6^7}=\frac{1}{6^3\cdot6^7}=\frac{1}{6^{3+7}}=\frac{1}{6^{10}}=6^{-10} \end{gathered}[/tex]so, this is an answer
Step 5
[tex]\begin{gathered} \frac{6^5\cdot6^{-3}}{6^{-8}} \\ \text{solve} \\ \frac{6^5\cdot6^{-3}}{6^{-8}}=\frac{6^{5-3}}{6^{-8}}=\frac{6^2}{6^{-8}}=6^2\cdot\frac{1}{6^{-8}}=6^2\cdot6^8=6^{10} \end{gathered}[/tex]so, this is not an answer
I hope this helps you
I need to double check 15 I got answer B
We will have that the area of one sector of the circle will be:
[tex]A=(\frac{45}{360})\pi(20in)^2\Rightarrow A=\frac{25\pi}{2}in^2[/tex]So, the solution is option B.
On the graph below, what is the length of side AB? B ...
The distance between two points in the plane is:
[tex]d(P,Q)=\sqrt[]{(x_2-x_1)^2+(y_2}-y_1)^2[/tex]The points A and B have coordinates A(5,3) and B(5,6). Then the distance between them is:
[tex]\begin{gathered} d(A,B)=\sqrt[]{(5-5)^2+(6-3)^2} \\ =\sqrt[]{(3)^2} \\ =\sqrt[]{9} \\ =3 \end{gathered}[/tex]Therefore, the length of the side AB is 3 units.
what is the slope intercept form of the line passing through the point (2,1) and having a slope of 4?
The equation of a line has the form:
[tex]y=mx+b[/tex]if the slope is equal to 4 then we know that: m = 4 and now we can replace the slope and the coordinate ( 2,1 ) to find b so:
[tex]\begin{gathered} 1=4(2)+b \\ 1-8=b \\ -7=b \end{gathered}[/tex]So the final equation will be:
[tex]y=4x-7[/tex]tom has a rectangular prism - shaped suitcase that measures 9 inches by 9 inches by 24 inches. he needs a second suitcase that has the same volume but smaller surface than his current suitcase. which suitcase size would fit Toms needs
ANSWER:
18 inches by 9 inches by 12 inches
EXPLANATION:
The volume of Tom's rectangular prism-shaped suitcase which measures 9 inches by 9 inches by 24 inches is;
[tex]\begin{gathered} Volume=l*w*h \\ \\ =9*9*24 \\ \\ =1944\text{ }square\text{ }inches \end{gathered}[/tex]So the volume of Tom's suitcase is 1944 cubic inches
The surface area will be;
[tex]\begin{gathered} SA=2(lw+wh+hl) \\ \\ =2(9*9+9*24+24*9) \\ \\ =2(81+216+216) \\ \\ =2(513) \\ \\ =1026\text{ }square\text{ }inches \end{gathered}[/tex]So the volume of the suitcase is 1026 square inches
*Let's go ahead and determine the volume and surface area of a suitcase that measures 18 inches by 18 inches by 6 inches;
[tex]\begin{gathered} Volume=l*w*h \\ \\ =18*18*6 \\ \\ =1944\text{ cubic inches} \end{gathered}[/tex][tex]\begin{gathered} Surface\text{ }Area=2(18*18+18*6+6*18) \\ \\ =2(324+108+108) \\ \\ =2(540) \\ \\ =1080\text{ square inches} \end{gathered}[/tex]We can see that the suitcase that measures 18 inches by 18 inches by 6 inches has the same volume as the first one but a higher surface area which doesn't fit Tom's needs
*Let's go ahead and determine the volume of a suitcase that measures 12 inches by 10 inches by 9 inches;
[tex]\begin{gathered} Volume=12*10*9 \\ \\ =1080\text{ cubic inches} \end{gathered}[/tex]We can see that the suitcase that measures 12 inches by 10 inches by 9 inches has a different volume from the first one which doesn't fit Tom's needs.
Let's go ahead and determine the volume of a suitcase that measures 16 inches by 5 inches by 9 inches;
[tex]\begin{gathered} Volume=16*5*9 \\ \\ =720\text{ cubic inches} \end{gathered}[/tex]We can see that the suitcase that measures 16 inches by 5 inches by 9 inches has a different volume from the first one which doesn't fit Tom's needs.
*Let's go ahead and determine the volume and surface area of a suitcase that measures 18 inches by 9 inches by 12 inches;
[tex]\begin{gathered} Volume=l*w*h \\ \\ =18*9*12 \\ \\ =1944\text{ cubic inches} \end{gathered}[/tex][tex]\begin{gathered} Surface\text{ }Area=2(18*9+9*12+12*18) \\ \\ =2(162+108+216) \\ \\ =2(486) \\ \\ =972\text{ square inches} \end{gathered}[/tex]We can see that the suitcase that measures 18 inches by 9 inches by 12 inches has the same volume as the first one and s smaller surface area which fits Tom's needs
Introduction to Probability
The probability of birthday being in July is 1/12.
What do you mean by probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a numeric value and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The likelihood that an event will occur increases with its probability. A straightforward illustration is flipping a fair (impartial) coin. The chance of either "heads" or "tails" is half because there are only two possible outcomes (heads or tails), and because the coin is fair, both outcomes (heads and tails) are equally likely.
Probability of birthday being in July = 1/12 (12 months in a year)
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rewrite using a single exponent. 9 4, 9 4
We need to represent the product of two exponents as one single exponent. To do that we need to calculate their product, when the bases are equal we can conserve the base and add the exponents. We will do this below:
[tex]9^49^4=9^{4+4}=9^8[/tex]The angle of depression from the top of a sheer cliff to point A on the ground is 35º. If point A is280 feet from the base of the cliff, how tall is the cliff? Round the answer to the nearest tenth of afoot.
In this case, to calculate the tall of the cliff, consider the distance from the base of the cliff to the point A, as a hypotenuse of a right triangle.
The tall of the clift is given by:
h = 280 sin(35)
h = 280(0.573)
h = 160.60
Hence, the tal of the clift is 160.60 feet
Suppose that the probability that you will win a contest is 0.0002, what is theprobability that you will not win the contest? Leave your answer as a decimal and donot round or estimate your answer.
Answer:
0.9998
Explanation:
The probability that you will not win the contest can be calculated as 1 less the probability that you will win a contest, so
1 - 0.0002 = 0.9998
Therefore, the answer is 0.9998
Find the volume of the figure. Round to the nearest hundredths place if necessary.
The volume of a Pyramid
Given a pyramid of base area A and height H, the volume is calculated as:
[tex]V=\frac{A\cdot H}{3}[/tex]The base of this pyramid is a right triangle, with a hypotenuse of c=19.3 mm and one leg of a=16.8 mm. The other leg can be calculated by using the Pythagora's Theorem:
[tex]c^2=a^2+b^2[/tex]Solving for b:
[tex]b^{}=\sqrt[]{c^2-a^2}=\sqrt[]{19.3^2-16.8^2}=9.5\operatorname{mm}[/tex]The area of the base is the semi-product of the legs:
[tex]A=\frac{16.8\cdot9.5}{2}=79.8\operatorname{mm}^2[/tex]Now the volume of the pyramid:
[tex]V=\frac{79.8\operatorname{mm}\cdot12\operatorname{mm}}{3}=319.2\operatorname{mm}^3[/tex]The volume of the figure is 319.2 cubic millimeters