A prime number is defined as a natural number which is only and only divisible by 1 and itself.
Note that 72 and 106 are even numbers, so they will have at least one factor as 2, which is neither 1 nor the number itself. Therefore, 72 and 196 cannot be a prime number.
Now, consider that 141 has the sum of digits as 6 which is divisible by 3, so according to the divisible rule of 3, the number 141 is divisible by 3, which is neither 1 nor the number itself. Therefore, 141 cannot be a prime number.
The last choice 107 do not possess any factor other than 1 and 107, so the number 107 is referred as a prime number.
Thus, option D is the correct choice.
If f(x) is an exponential function where f(3.5)=12, and f(9)=75 then find the value of f(7.5) to the nearest hundredth?
Given the general exponential function:
[tex]f(x)=A\cdot b^x[/tex]Where A and b are parameters. Then, using the information provided in the problem:
[tex]\begin{gathered} f(3.5)=A\cdot b^{3.5}=12 \\ f(9)=A\cdot b^9=75 \end{gathered}[/tex]Taking the division:
[tex]\begin{gathered} \frac{A\cdot b^9}{A\cdot b^{3.5}}=\frac{75}{12} \\ b^{5.5}=6.25 \\ \Rightarrow b=1.39542 \end{gathered}[/tex]Now, we use f(9) = 75 to find the parameter A:
[tex]\begin{gathered} f(9)=A\cdot1.39542^9=75 \\ \Rightarrow A=3.7386 \end{gathered}[/tex]The function is:
[tex]f(x)=3.7386\cdot1.39542^x[/tex]We evaluate at x = 7.5:
[tex]\begin{gathered} f(7.5)=3.7386\cdot1.39542^{7.5} \\ \Rightarrow f(7.5)=45.50 \end{gathered}[/tex]What are the new coordinates of these pre-image points after a 90° CCW rotation? A (-3,2), B (4, -7), C (-9,-8)
The 90 degree counter clockwise Rotation can be represented by the rule;
[tex](x,y)\rightarrow(-y,x)[/tex]Given the points A, B and C, applying the rule to each we have;
[tex]undefined[/tex]you like to watch at the local cinema. you have to payment options A is to hit a discount which will cost 160 a d then 20 per movie options b pays 40 per movie what will the total cost of the two options
Let x be the number of movies you watch.
Option A will cost you:
[tex]20x+160[/tex]Option B will cost you:
[tex]40x[/tex]The two options will cost the same when:
[tex]\begin{gathered} 20x+160=40x \\ 160=40x-20x \\ 20x=160 \\ x=\frac{160}{20} \\ x=8 \end{gathered}[/tex]Therefore, after 8 movies the two options will cost the same.
I need help with the attached question. Another tutor was working with me and we lost connectivity. We determined perimeter is calculated adding all sides together but I missed a few of his points just before the final solution
In order to determine the perimeter of the figure, first simplify the radicals, as follow:
2√20 = 2√(5*2^2) = 4√5
4√12 = 4√(3*2^2) = 8√3
2√48 = 2√(3*2^4) = 8√3
√80 = √(5*2^4) = 4√5
Now, add the previous results:
P = 4√5 + 8√3 + 8√3 + 4√5 = 8√5 + 16√3
Hence, the perimeter of the figure is 8√5 + 16√3 inches
If wallpaper costs $1.25 per squared foot, how much will it cost to put new wallpaper in a room with area dimensions of 17 ft long by 16 ft wide?
Calculate the area of the wall using the formula for the area of a rectangle:
[tex]A=b\times h[/tex]Then:
[tex]\begin{gathered} A=(17ft)(16ft) \\ =272ft^2 \end{gathered}[/tex]Since each square foot of wallpaper costs $1.25, multiply 272 times 1.25 to find the total cost of covering the rectangular wall:
[tex]272\times\text{1}.25=340[/tex]Therefore, the total cost would be $340 for one wall.
The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 eachand adult tickets cost $4 each. If the total receipts were $1740, how many students attendedthe talent show?
In total 530 tickets
Students tickets cost $3
Adult tickets cost $4
in total receipts were $1740
x= students
y=adults
we can have the next two equations
x+y=530
3x+4y=1740
we can rewrite the first equation
x=530-y
we substitute the equation above in the second equation
[tex]\begin{gathered} 3(530-y)+4y=1740 \\ 1590-3y+4y=1740 \\ y=1740-1590 \\ y=150 \end{gathered}[/tex]then we substitute the value of y in x=530-y
[tex]\begin{gathered} x=530-150 \\ x=380 \end{gathered}[/tex]In total 380 students attended the talent show
Answer:
380
Step-by-step explanation:
It is 1.9 miles from a house to a restaurant and 1.2miles to a pier, as shown at the right. The anglebetween the two lines of sight is 87°. How far is it fromthe pier across the water to the restaurant.
Since two side sides of the triangle and an angle is known, we apply the Cosine rule
Formula for Cosine rule is given below,
Where a is distance between the house and pier,
b is the distance between the house and restaurant,
c is the distance between the pier and the restaurant,
C is the angle opposite c
[tex]c^2=a^2+b^2-2ab\cos C[/tex][tex]\begin{gathered} \text{Where,} \\ a=1.2\text{ miles} \\ b=1.9\text{ miles and } \\ c=unknown^{} \\ C=87^0 \end{gathered}[/tex]Substituting the variables into the given formula above,
[tex]\begin{gathered} c^2=a^2+b^2-2ab\cos C \\ c^2=(1.2)^2+(1.9)^2-2(1.2)(1.9)\cos 87^0 \\ c^2=1.44+3.61-4.56(0.05234) \\ c^2=5.05-0.2387 \\ c^2=4.8113 \\ \sqrt[]{c^2}=\sqrt[]{4.8113} \\ c=2.1935\text{ miles} \\ c\approx2.19\text{ miles} \end{gathered}[/tex]Hence, the distance from the pier to the restaurant is 2.19 miles.
Find the permeter of the figure 2x 3x - 1 5x + 4
We are given a figure and asked to find the perimeter.
Recall that the perimeter of a figure is the sum of all of its lengths.
Since we are given the lenghts of the sides of the figure, let us add them together to find the perimeter.
[tex]P=(2x)+(3x-1)+(5x+4)_{}[/tex]Simplify the equation
[tex]\begin{gathered} P=2x+3x-1+5x+4 \\ P=2x+3x+5x-1+4 \\ P=10x-1+4 \\ P=10x+3 \end{gathered}[/tex]Therefore, the perimeter of the given figure is
[tex]P=10x+3[/tex]Option C is the correct answer.
May I please get help with this math. I need help figuring out the lengths and whether they can be a sides of a triangle
we know that there are three type of traingles based on the length of sides
Equilateral, isosceles and scalene .
we used pythagorean theorem to find the lengths of the traigle
longest length in a traingle known as hypotenious .
there are two other lengths base and perpendicular
Find the measures of the labeled angles. (x +116)° =..... ° (Type a whole number.) 5x = ....°(Type a whole number.)
We know that the two angles with measures (x+116) and (5x) have the same measure, as they are vertical angles.
Then, we can write:
[tex]\begin{gathered} x+116=5x \\ x-5x=-116 \\ -4x=-116 \\ x=\frac{-116}{-4} \\ x=29 \end{gathered}[/tex]With the value of x, we can find the measure of both angles, as they have the same measure:
[tex]5x=5\cdot29=145[/tex]Answer:
(x +116)° = 145°
5x = 145°
Solve the system of two linear inequalities graphically. Find the region with points that satisfy both any qualities.
Given the system of inequalities
[tex]\begin{gathered} x>4 \\ y\ge-6 \end{gathered}[/tex]The first inequality is a vertical dashed line at x = 4
And the second inequality is a horizontal solid line at y = -6
the shaded region will be as shown in the following picture:
So, the answer will be option A
which rational number also belongs to the set of natural numbers. 9, 1/4, -9 or 0.933........
Note that natural numbers are integer values that are greater than 0. They can also be called positive integers or counting numbers
Out of all the rational numbers given, only 9 is a positive integer, hence it
Determine the volume of the rectangular prism show 6.4 in. 5.1 in 10.2 in.
The volume of the rectangular prism is 332.928 cubic inches
Here, we want to calculate the volume of the prism shown
To calculate the volume of the prism, we calculate the area of the base and multiply by the height of the prism
The base of the prism is a rectangle that measures 6.4 inches by 5.1 inches
The area of the base is thus;
[tex]A\text{ = 6.4 }\times\text{ 5.1 = 32.64 square inches}[/tex]Now, to complete the calculation of the volume, we shall multiply this area by the height
The height as seen by the given figure is 10.2 inches
Thus, the volume of the prism is;
[tex]V\text{ = 32.64}\times\text{ 10.2 = 332.928 cubic inches}[/tex]Find P (X > 80) if X follows a normal distribution with a mean of 75 and a standard deviation of 5.
Given that X follows a normal distribution with a mean of 75 and a standard deviation of 5;
Using the Z-value formula;
[tex]Z=\frac{X-\mu}{\sigma}[/tex]Given;
[tex]undefined[/tex]Write2796asaRomanNumeral.
the roman numeral of 2796 is MMDCCXCVI.
Determine if the order pairs is part of the solution
The given equation is expressed as
x + 3y = 6
To determine wether the ordered pairs are solutions of the equation, we would substitute the values of x and y in the ordered pairs into the equation. If both sides of the equation are equal, then the ordered pair is a solution. We have
a) For a = 3 and y = 1, we have
3 + 3(1) = 6
3 + 3 = 6
6 = 6
It is a solution
b) For x = 6 and y = 0
6 + 3(0) = 6
6 + 0 = 6
6 = 6
It is a solution
c) - 2 + 3(2/3) = 6
- 2 + 2 = 6
0 is not equal to 6
It is not a solution
The correct answers are options a and b
Make sure to plot both lines the relation and its inverse
Given the equation of the line
[tex]y=3x-5[/tex]We can use the x, and y-intercept to plot the graph
[tex](0,-5)and(\frac{5}{3},0)[/tex]
We can obtain the inverse as follow:
[tex]\begin{gathered} \text{make x the subject of the formula} \\ 3x=y+5 \\ x=\frac{y+5}{3} \end{gathered}[/tex]Thus, the inverse of y will be
[tex]f^{-1}(x)=\frac{x+5}{3}[/tex]similarly, we can get the x and y-intercept
[tex](-5,0)\text{and(}0,\frac{5}{3}\text{)}[/tex]The plot can be shown as
square pyramid volume 225 cubic inches , base Edge 5 in
Square pyramid volume 225 cubic inches , base Edge 5 in
hi
what is your question
__________________________
Square pyramid volume = a^2 * h/3
225= 5^2 * h / 3
h* 5^2 = 225*3
h* 25 = 225*3
h= 225*3/25
h=27 in
_______________________________________
The height of the square pyramid is 27 in
Do you have any questions regarding the solution?
Determine the lateral and total surfacearea of the pyramid.
ANSWER
• Lateral surface area: ,73 cm²
,• Total surface area: ,93 cm²
EXPLANATION
The lateral surface area is the sum of the areas of the triangles. There are two triangles with dimensions: base = 4cm, height = 8cm and two triangles with dimensions: base = 5cm, height = 8.2cm.
The lateral surface area LSA is:
[tex]\begin{gathered} \text{LSA}=2\cdot(\frac{4\cdot8}{2})+2\cdot(\frac{5\cdot8.2}{2}) \\ \text{LSA}=4\cdot8+5\cdot8.2 \\ \text{LSA}=73\operatorname{cm}^2 \end{gathered}[/tex]The total surface area SA is the LSA plus the area of the base of the pyramid, which is a rectangle with dimensions: 4cm x 5cm:
[tex]\begin{gathered} SA=\text{LSA}+4\cdot5 \\ SA=73\operatorname{cm}+20\operatorname{cm}^2 \\ SA=93\operatorname{cm}^2 \end{gathered}[/tex]use the points 50,25 and 200,100 to calculate the slope
The slope of the line that passes through the points (x1, y1) and (x2, y2) is computed as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this case, the points are (50,25) and (200,100), then the slope is:
[tex]m=\frac{100-25}{200-50}=\frac{75}{150}=\frac{1}{2}[/tex]1. To make a strawberry and blackberry smoothie, mix 3 ounces of strawberrywith 1/3 cups of blackberry. How much strawberry do we mix with 3 cups ofblackberry ?
Answer:
27 ounces of strawberry
Explanation:
Let x represent the amount of strawberry needed.
We can go ahead and solve for x by setting up proportions as follows;
[tex]\begin{gathered} 3\text{ ounces of strawberry}\rightarrow\frac{1}{3}\text{ cups of blackberry} \\ x\rightarrow3\text{ cups of blackberry} \\ \frac{x}{3}=3\times3 \\ x=9\times3 \\ x=27\text{ ounces of strawberry} \end{gathered}[/tex]How many pennies, how many dimes,how many nickels, and how many quarters
Let n represents the number of nickel
Let p represents the number of pennies
Let d represents the number of dimes
Let q represents the number of quarters
Recall that
1 nickel = $0.05
1 penny = $0.01
1 dime = $0.1
1 quarter = $0.25
From the information given,
n + p + d + q = 12-------------------------------------------------(1)
0.05n + 0.01p + 0.1d + 0.25q = 1.67-------------------------(2)
p = n --------------------------------------------------------------------(3)
n + d = q ----------------------------------------------------------------(4)
Solving the four equations simultaneously, we have
Substitute equations (3) and (4) into equations (1) and (2)
n + n + d + n + d = 12
0.05n + 0.01n + 0.1d + 0.25(n + d) = 1.67
3n + 2d = 12-----------------------------------------(5)
0.31n + 0.35d = 1.67--------------------------------(6)
multiply equation (6) by 200 and equation (5) by 35, we have
105n + 70d=420------------------(7)
62n + 70d =334--------------------(8)
subtract equation (8) from (7)
43n = 86
n=86/43
n=2
put n=2 into equation (8)
62(2) + 70d = 334
124 + 70d = 334
70d = 334 - 124
70d = 210
d = 210/70
d=3
but p = n = 2
p = 2
n + d = q
q = 2 + 3 = 5
Hence, max have
2 nickels, 2 pennies, 3 dimes, 5 quarters
2. (-4, 8), (-1, 2), (2, -4), (5, -10) is it a function and why??
Answer:
Its an function
Step-by-step explanation:
Since there is one value of y for every value of x
x
in standard form, the line parallel to the shown line and passing through the origin.
The equation of a line in standard form is written as:
[tex]Ax+By=C[/tex]Now, two lines are parallel if and only if their slopes are equal, that is:
[tex]m_1=m_2[/tex]The slope of a line is given by:
[tex]m=\frac{y_2-y_1_{}}{x_2-x_1}[/tex]where (x1,y1) and (x2,y2) are points through the line. From the graph we notice that the line passes through the points (0,3) and (5,-1) then its slope is:
[tex]\begin{gathered} m=\frac{-1-3}{5-0} \\ m=-\frac{4}{5} \end{gathered}[/tex]This means that the lin in the graph has a slope os -4/5 and hence the paralell line we are looking for has slope -4/5 as well.
Once we know the slope of the line we want we just need a point; the porblem states that the line passes through the origin, then it passes through the point (0,0). The equation of a line with slope m that passes throught the point (x1,y1) is given by:
[tex]y-y_1=m(x-x_1)[/tex]Plugging the values of the slope and the point we have that:
[tex]\begin{gathered} y-0=-\frac{4}{5}(x-0) \\ y=-\frac{4}{5}x \end{gathered}[/tex]Finally we just write the equation in standard form, therefore the equation of the line is:
[tex]\frac{4}{5}x+y=0[/tex]The two options are x > 1, x < 1which one is it?
In a inequality you have next sings:
< (less than) and ≤ (less than or equal to)
> (greather than) and ≥ (greather tan or equal to)
To graph the first pair of sings you draw a line to the left of the given number
To grpah the second pair of sings you draw a line to the right of the given number
In this case you have a line to the left of 1 (as the point in 1 is not a filled point it menas that the answer doesn't include the 1).
Then, the given graph is for the inequality: x<1BDGiven:BC||AD.List congruence statements based on the given information.Angle ABD is congruent to angle BDCOBD = BDOBC = ADO AB = DCAngle ADB is congruent to angle DBC
* Angle ABD is congruent to angle BDC
False: There is no enough information to conclude it
-------------------------------------------------------------
*BD = BD
True: Because of reflexive property.
-------------------------------------------------------------
*BC = AD
False: There is no enough information to conclude it
-------------------------------------------------------------
*AB = DC
False: There is no enough information to conclude it
-------------------------------------------------------------
* Angle ADB is congruent to angle DBC
True: They are alternate interior angles.
Answer:
The only valid choices are:
BD = BD
Angle ADB is congruent to angle DBC
Find the fourth term of the binomial expansion(2x + y)^7
In order to find the appropriate coefficients for the binomila expansion in the case of such high exponent, it is convenient to use Pascal's triangle .
I am pasting an image of a Pascal triangle up to the power 7 below:
Notice that the coefficients are lasted from left to right as the first one with power 7 for the 2x term, and no inclusion of the term y, and then decreasing the power of the 2x term, as the term in y increases power.
That is, the terms ordered from highest in 2x to lower go like:
(2x)^7 + 7 (2x)^6 (y) + 21 (2x)^5 (y)^2 + 35 (2x)^4 (y)^3 + ...
We stop here since we are asked specifically for the fourth term, which is:
35 (2x)^4 (y)^3 = 35 * 16 x^4 y^3 = 560 x^4 y^3
Change a Relation to Make It a FunctionThe relation R is shown below as a list of orderedpairs.R= {(1, 4), (1, 3), (-1, 3), (2, 15) }Which ordered pairs prevent this relation frombeing a function?(1, 4) and (1, 3), because they have thesame x-valueO (1, 3) and (-1, 3), because they have thesame y-valueDONE
For a function, an input or value of x must not have more than one output or value of y. Considering the given relation,
R= {(1, 4), (1, 3), (-1, 3), (2, 15) }
The input value of x = 1 corresponds to two output values of y = 3 and y = 4
Thus, the ordered pairs that prevent this relation from being a function is
(1, 4) and (1, 3), because they have the same x-value
To the nearest tenth, What is the area of a shaded segment when AG= 6 ft
28.3 square feet
Explanations:
The formula for calculating the area of the shaded segment is expressed as:
[tex]A=\frac{1}{2}\times r^2(\theta-sin\theta)[/tex]where:
r is the radius = AG = 6ft
θ = 90 degrees
Substitute the given parameter into the formula
[tex]\begin{gathered} A=\frac{1}{2}\times6^2(\frac{\pi}{2}-sin(\frac{\pi}{2})) \\ A=\frac{1}{2}\times36(\frac{\pi}{2}-1) \\ A=18(\frac{\pi}{2}-1) \\ \end{gathered}[/tex]Since π = 3.14, then;
[tex]\begin{gathered} A=18(\frac{3.14}{2}-1) \\ A=18(1.57-1) \\ A=18(0.57) \\ A=28.26 \\ A\approx28.3ft^2 \end{gathered}[/tex]Hence the area of the shaded region is 28.3 square feet
write the explicit formula for the following sequence then find the 7th term 500, 100, 20, 4
The first term of sequence is a = 500.
Determine the common ratio for the sequence.
[tex]\begin{gathered} r=\frac{500}{100} \\ =5 \end{gathered}[/tex]The general explicit formula is,
[tex]a_n=a(r)^{n-1}_{}[/tex]Here n is position of term in sequence.
Substitute the value of a and r in the sequence to obtain explicy formula of sequence.
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