Answer:
$6.50
Step-by-step explanation:
Let the cost of a bowl and a jug be $b and $j respectively.
3b +j= 13.70 -----(1)
j= b +4.10 -----(2)
Substitute (2) into (1):
3b +b +4.10= 13.70
4b +4.10= 13.70 (simplify)
4b= 13.70 -4.10 (-4.10 on both sides)
4b= 9.60
b= 9.60 ÷4 (÷4 on both sides)
b= 2.40
Substitute b= 2.40 into (2):
j= 2.40 +4.10
j= 6.50
Thus, the jug costs $6.50.
According to the rules of Major League Baseball, the infield must be 30 feet by 30 feet in a diamond shape with perpendicular (90°) corners. Answer the following questions regarding the shape of the infield.
Answer:
No Major League ballparks are exactly alike, but certain aspects of the field of play must be uniform across baseball.
The infield must be a square that is 90 feet on each side, and the outfield is the area between the two foul lines formed by extending two sides of said square (though the dirt portion of the field that runs well past the 90-foot basepaths in all Major League parks is also commonly referred to as the infield). The field must be constructed so that the bases are the same level as home plate.
The rulebook states that parks constructed by professional teams after June 1, 1958, must have a minimum distance of 325 feet between home plate and the nearest fence, stand or other obstruction on the right- and left-field foul lines, and 400 feet between home plate and the nearest fence, stand or other obstruction in center field. However, some clubs have been permitted to construct parks after that date with dimensions shorter than those specified.
The pitcher's plate must be a 24-inch by 6-inch slab of whitened rubber that is 10 inches above the level of home plate and 60 feet, 6 inches away from the back point of home plate. It is placed 18 inches behind the center of the mound -- which is erected within an 18-foot diameter circle -- and surrounded by a level area that is 5 feet by 34 inches. The slope of the pitcher's mound begins 6 inches in front of the pitcher's plate and must gradually decrease by 1 inch every foot for 6 feet in the direction of home plate.
Home plate is a 17-inch square of whitened rubber with two of the corners removed so that one edge is 17 inches long, two adjacent sides are 8 1/2 inches each and the remaining two sides are 12 inches each and set at an angle to make a point. The 17-inch side faces the pitcher's plate, and the two 12-inch edges coincide with the first- and third-base lines. The back tip of home plate must be 127 feet, 3 and 3/8 inches away from second base.
The other bases must be 15-inch squares that are between 3 and 5 inches thick, covered by white canvas or rubber and filled with soft material.
Step-by-step explanation:
Identify the equation of the circle that has its center at (16, 30) and passes through the origin
To solve this question, we have to find the equation of the circle with given center and where it passes. Doing this, we get that the equation of the circle is:
[tex](x - 16)^2 + (y - 30)^2 = 1156[/tex]
Equation of a circle:
The equation of a circle with center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
Center at (16, 30)
This means that [tex]x_0 = 16, y_0 = 30[/tex]
Thus
[tex](x - 16)^2 + (y - 30)^2 = r^2[/tex]
Passes through the origin:
We use this to find the radius squared, as this means that [tex]x = 0, y = 0[/tex] is part of the circle. Thus
[tex](x - 16)^2 + (y - 30)^2 = r^2[/tex]
[tex](0 - 16)^2 + (0 - 30)^2 = r^2[/tex]
[tex]r^2 = 16^2 + 30^2 = 1156[/tex]
Thus, the equation of the circle is:
[tex](x - 16)^2 + (y - 30)^2 = 1156[/tex]
For another example to find the equation of a circle, you can look at https://brainly.com/question/23719612
Find the 8th term of the geometric sequence 7,−21,63,
Answer:
8th term is -15309
Step-by-step explanation:
[tex]{ \boxed{ \bf{u_{n} = a( {r}^{n - 1} ) }}} \\ { \tt{u_{8} = 7( {( - 3)}^{8 - 1}) }} \\ { \tt{u_{8} = 7( - 2187)}} \\ { \tt{u _{8} = - 15309}}[/tex]
r is the common difference, r = -21/7 = -3
Answer:
a₈ = - 15309
Step-by-step explanation:
The nth term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Here a₁ = 7 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-21}{7}[/tex] = - 3 , then
a₈ = 7 × [tex](-3)^{7}[/tex] = 7 × - 2187 = - 15309
graph the equation y=5/7x
Answer:
Step-by-step explanation:
The report "Digital Democracy Surveyt describes a large national survey. In a representative sample of Americans ages 14 to 18 years, 45% indicated that they usually use social media while watching
TV. Suppose that the sample size was 760.
(a) Is there convincing evidence that less than half of Americans ages 14 to 18 years usually use social media while watching TV? Use a significance level of 0.05.
State the appropriate null and alternative hypotheses.
O Hop 0.5 versus Hp > 0.5
O Moip 0.5 versus H: = 0.5
O Hp = 0.5 versus HP < 0.5
OH:P < 0.5 versus , p > 0.5
OHOD 0.5 versus H: 0.5
Find the test statistic and P-value. (Use a table or technology. Round your test statistic to two decimal places and your p-value to four decimal places.)
ZE
P-value
Answer:
H0 : p = 0.5 versus H1: P < 0.5
Test statistic = - 2.76
Pvalue = 0.0029
Step-by-step explanation:
The hypothesis :
We are to test if less Than half of the American population within the of 14 to 18 years usually use social media while watching TV :
Hence, population proportion, p = 0.5
H0: p = 0.5
H1: P < 0.5
Sample size, n = 760
Sample proportion, Phat = 45% = 0.45
The test statistic, Z :
Z = (Phat - P) / √[(P(1 - P)) /n]
Z = (0.45 - 0.5) / √[(0.5(1 - 0.5)) /760]
Z = - 0.05 / √0.0003289
Z = - 2.7568 ; Z = - 2.76 (2 decimal places)
The Pvalue :
Using technology :
Pvalue from Zscore calculator ; Pvalue = 0.0029
Decision region :
Reject H0 if Pvalue < α
α = 0.05
Since 0.0029 < 0.05 ; we reject the Null and conclude that less than half of American within age 14 to 18 years usually use social media while watching TV.
If cos(27) =p, express sin(27) in terms of p
Answer:
√(p²-1)
Step-by-step explanation:
sin (27°) = √(p²-1) / 1
= √(p²-1)
What is an
equation of the line that passes through the points (-3,-1) and (-4,-4)
Answer:
y= 3x+8
Step-by-step explanation:
not a 100% sure...
sry if its wrong
(try using Math-way, its rly helpful)
Answer:
Step-by-step explanation:
y=mx+b
To find slope: -4+1/-4+3
Slope=3
y=3x+b
Plug in either points ,as an example, i'll plug in (-3,-1)
-1=3(-3)+b
-1=-9+b
8=b
Finished formula: y=3x+8
Angie used 4 apples and 5 strawberries in her fruit salad. Salim used 7 apples and 9 strawberries. Did Angie and Salim use the same ratio of apples to strawberries? If not, who used the greater ratio of apples to strawberries?
Answer:
We can write a ratio between two quantities, x and y, as:
x to y.
To find if two ratios:
"a to b" and "c to d" are equal, we need to see if the quotientes:
a/b and c/d are equal.
Here we know that the ratios are:
4 apples to 5 strawberries, this gives the quotient 4/5 = 0.8
7 apples to 9 strawberries, this gives the quotient 7/9 = 0.78
So the quotients are different, which means that the ratios are not equal.
Now we want to see who used a greater ratio of apples to strawberries.
notice that in the numerator we used the number of apples, so as larger is the quotient, larger is the ratio of apples to strawberries.
We can see that the quotient of Angie is larger, then Angie used the greater ratio of apples to strawberries.
You have $475 in your savings account that earns 3.25% simple interest each year. How much interest will you accumulate after 7 years?
Answer:
$613.45
Step-by-step explanation:
Multiply $475 by 3.25% of it and so on 7 times, which adds up to 613.4993293. Round that to 613.45
PLEASE HELP WILL GIVE BRAILNLIEST! Find the value of x
Answer:
x = 14.63
Step-by-step explanation:
hurryyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
Answer:
D. II & III
Step-by-step explanation:
II (x - 4)(2x + 9) = 2x² + x - 36
III (x - 4)(x - 6) = x²- 10x + 24
I has factors (x + 4)(x - 8)
IV has factors x(x - 16)
Jennifer invested $379 in a simple interest account. The account now has $554 in it. The money has been invested for 5 years. What interest rate (as a percentage) did this account have?
9514 1404 393
Answer:
9.23%
Step-by-step explanation:
The account balance for simple interest is given by ...
A = P(1 +rt) . . . . . principal P invested for t years at rate r
554 = 379(1 +r·5)
554 = 379 + 1895r . . . . eliminate parentheses
175 = 1895r . . . . . . . . . subtract 379
r = 175/1895 ≈ 0.092348 ≈ 9.23%
Jennifer's account had an interest rate of about 9.23%.
The triangle on the grid will be translated two units down.
On a coordinate plane, triangle A B C has points (2, 1), (0, negative 1), (2, negative 1).
Which shows the triangle when it is translated two units down?
On a coordinate plane, triangle A prime B prime C prime has points (0, negative 1), (0, negative 3), (2, negative 3).
On a coordinate plane, triangle A prime B prime C prime has points (0, 1), (negative 2, negative 1), (0, negative 1).
On a coordinate plane, triangle A prime B prime C prime has points (2, negative 1), (2, negative 3), (0, negative 3).
On a coordinate plane, triangle A prime B prime C prime has points (2, negative 1), (2, negative 3), (0, negative 1).
Given:
The vertices of the triangle ABC are A(2, 1), B(0,-1), C(2, -1).
To find:
The vertices of the image of triangle ABC if ABC is translated two units down.
Solution:
It is given that the triangle ABC is translated two units down. So, the rule of translation is:
[tex](x,y)\to (x,y-2)[/tex]
Using this rule, we get
[tex]A(2,1)\to A'(2,1-2)[/tex]
[tex]A(2,1)\to A'(2,-1)[/tex]
Similarly,
[tex]B(0,-1)\to B'(0,-1-2)[/tex]
[tex]B(0,-1)\to B'(0,-3)[/tex]
And,
[tex]C(2.-1)\to C'(2,-1-2)[/tex]
[tex]C(2.-1)\to C'(2,-3)[/tex]
The vertices of the image are A'(2,-1), B'(0,-3), C'(2,-3).
Therefore, the correct option is C.
Answer:
C.
Step-by-step explanation:
What is 2:50 is simplest form
Answer:
0.04
Step-by-step explanation:
2 / 50 is the same as 1 / 25.
1 / 25 = 0.04
Answer:
0.04
Step-by-step explanation:
PLEASE HELP! I HAVE BEEN AT THIS FOR A LONG TIME!.
For each investement, 25 000 is deposited in an account. How much is each payment?
(a. 8% per annum, compounded annually, with annual payments starting in a year.
Answer:
Annual payment wil be 2,001 and total amount after compounded annually will be 27,001
Find the general solution for:-
[tex]sin\:x \:cos\: 3x+cos\:x\: sin\:3x=tan140[/tex]
~Please show your work
~Thank you!
Answer:
[tex] \rm \displaystyle x \approx \bigg \{ {59.3}^{ \circ} + \frac{n\pi}{2} , - {14.3}^{ \circ} + \frac{n\pi}{2} \bigg \}[/tex]
Step-by-step explanation:
we would like to solve the following trigonometric equation:
[tex] \rm \displaystyle \sin(x) \cos(3x) + \cos(x) \sin(3x) = \tan( {140}^{ \circ} ) [/tex]
the left hand side can be rewritten using angle sum indentity of sin which is given by:
[tex] \rm \displaystyle \sin( \alpha + \beta ) = \sin( \alpha ) \cos( \beta ) + \cos( \alpha ) \sin( \beta ) [/tex]
therefore Let
[tex] \alpha = x[/tex][tex] \beta = 3x[/tex]Thus substitute:
[tex] \rm \displaystyle \sin(x + 3x) = \tan( {140}^{ \circ} ) [/tex]
simplify addition:
[tex] \rm \displaystyle \sin(4x) = \tan( {140}^{ \circ} ) [/tex]
keep in mind that sin(t)=sin(π-t) saying that there're two equation to solve:
[tex] \begin{cases} \rm \displaystyle \sin(4x) = \tan( {140}^{ \circ} ) \\ \\ \displaystyle \sin(\pi - 4x) = \tan( {140}^{ \circ} ) \end{cases}[/tex]
take inverse trig and that yields:
[tex] \begin{cases} \rm \displaystyle 4x= { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) \\ \\ \displaystyle \pi - 4x = { \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) \end{cases}[/tex]
add π to both sides of the second equation and that yields:
[tex] \begin{cases} \rm \displaystyle 4x= { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) \\ \\ \displaystyle - 4x = { \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) + \pi\end{cases}[/tex]
sin function has a period of 2nπ thus add the period:
[tex] \begin{cases} \rm \displaystyle 4x= { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) + 2n\pi\\ \\ \displaystyle - 4x = { \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) + \pi + 2n\pi\end{cases}[/tex]
divide I equation by 4 and II by -4 which yields:
[tex] \begin{cases} \rm \displaystyle x= \frac{ { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) }{4} + \frac{n\pi}{2} \\ \\ \displaystyle x = - \frac{{ \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) + \pi}{4} - \frac{n\pi}{2} \end{cases}[/tex]
recall that,-½(nπ)=½(nπ) therefore,
[tex] \begin{cases} \rm \displaystyle x= \frac{ { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) }{4} + \frac{n\pi}{2} \\ \\ \displaystyle x = - \frac{{ \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) + \pi}{4} + \frac{n\pi}{2} \end{cases}[/tex]
by using a calculator we acquire:
[tex] \begin{cases} \rm \displaystyle x \approx - {14.3}^{ \circ} + \frac{n\pi}{2} \\ \\ \displaystyle x \approx {59.3}^{ \circ} + \frac{n\pi}{2} \end{cases}[/tex]
hence,
the general solution for: for the trig equation are
[tex] \rm \displaystyle x \approx \bigg \{ {59.3}^{ \circ} + \frac{n\pi}{2} , - {14.3}^{ \circ} + \frac{n\pi}{2} \bigg \}[/tex]
If the diameter of a cylinder is 18 inches, the radius of the cylinder is 9 inches.
True False
Answer:
True
Step-by-step explanation:
A cylinder has two circles as its bases, and the diameter formula is:
2r = d
So if you plug in:
2r = 18
--- ---
2 2
r = 9
So it will be true.
Hope this helped.
What is the equation of the line that is perpendicular to the line y = 2x + 5 and
passes through the point (-4, 2)?
Answer:
y = -1/2x
Step-by-step explanation:
If two lines are perpendicular to each other, they have opposite slopes.
The first line is y = 2x + 5. Its slope is 2. A line perpendicular to this one will have a slope of -1/2.
Plug this value (-1/2) into your standard point-slope equation of y = mx + b.
y = -1/2x + b
To find b, we want to plug in a value that we know is on this line: in this case, it is (-4, 2). Plug in the x and y values into the x and y of the standard equation.
2 = -1/2(-4) + b
To find b, multiply the slope and the input of x (-4)
2 = 2 + b
Now, subtract 2 from both sides to isolate b.
0 = b
Plug this into your standard equation.
y = -1/2x + 0 or y = -1/2x
This equation is perpendicular to your given equation (y = 2x + 5) and contains point (-4, 2)
Hope this helps!
Which linear inequality is represented by the graph?
Answer:
D
Step-by-step explanation:
The correct answer is D
Answer:
D
Step-by-step explanation:
y<2/3 x-1 is the answer
A baker finds several new recipes to try. Of the new recipes, there are 11 for cookies, 10 for muffins, and 4 for cakes. If the baker selects a recipe at random, what is the probability the recipe is for a cake?
Answer:
4/25
Step-by-step explanation:
All the amount of recipes is 11+10+4=25 . There are 4 recipes for cakes
so probability is 4/25
equation of the line which passes through point (0,5) at gradient of - 1
Answer:
y = - x + 5
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here gradient (slope) = - 1 and (0, 5) ⇒ c = 5
y = - x + 5 ← equation of line
The average age of a preschool class is 4.5 years old. If there is one 3-year-old, five 5-year-olds, and two other children both of the same age, what is the age, in years, of the other two children?
Answer:
3.1
Step-by-step explanation:
5 x5 =25
25+3=28
the other children are 4 years old
simplify (2^2×4^-2)×5^8+2+3^0
volume of a cuboid whose edges are 4 cm, 5 cm and 6 cm
Answer:
120
Step-by-step explanation:
Formula for cuboid: L × W × H
Plug in:
L × W × H
4 × 5 × 6
^ ^
20 × 6
^ ^
120
Hope this helps.
Rewrite the radical expression as an expression with rational exponents.
cube root of x to the power of 8
Answer:
Step-by-step explanation:
[tex]\sqrt[3]{x^8}=x^{\frac{8}{3}[/tex] The little number outside is called the index and that always serves as the denominator in the rational exponent. The power on the radicand (the radicand is whatever is inside the radical) serves as the numerator.
A regular square pyramid has a slant height of 5 in and a base area of 49 in2. Find the surface area of the pyramid. ------------------------------------------------------------------------------------------- 171.5 square inches 70 square inches 119 square inches 245 square inches
Answer:
C: 119 square inches
Step-by-step explanation:
We are given;
Slant height; L = 5 in
Base area; B = 49 in²
Since it's a square pyramid, the base portion has a square shape.
Thus, area of base = x²
Where x is a side of the square.
Thus;
x² = 49
x = √49
x = 7
Perimeter of base = 7 × 4 = 28 in
Area of pyramid = ½PL + B
Plugging in the relevant values;
Area of pyramid = (½ × 28 × 5) + 49
Area of pyramid = 119 in²
_(9)=(2(1-2(2)^(9)))/(1-2(2))
PLEASE HELP ME OUT.
Answer:
the answer = um ok
Step-by-step explanation:
Any help, I would highly appreciate it
Answer:
B
Step-by-step explanation:
We are given the equation:
[tex]\displaystyle x(b-c) = y+x[/tex]
And that:
[tex]2b=3c=7[/tex]
And we want to find the value of y / x.
To start, subtract x from both sides in the first equation:
[tex]x(b-c) -x = y[/tex]
Divide both sides by x:
[tex]\displaystyle \frac{x(b-c)-x}{x}=\frac{y}{x}[/tex]
Simplify:
[tex]\displaystyle (b-c)-1 = \frac{y}{x}[/tex]
Next, in the second equation, divide everything by two:
[tex]\displaystyle b = \frac{3}{2} c = \frac{7}{2}[/tex]
Substitute:
[tex]\displaystyle \left(\frac{3}{2} c - c \right) - 1= \frac{y}{x}[/tex]
Simplify:
[tex]\displaystyle \frac{1}{2} c - 1 = \frac{y}{x}[/tex]
From the modified second equation, we can multipy both sides by 1/3:
[tex]\displaystyle \frac{1}{2} c = \frac{7}{6}[/tex]
Substitute:
[tex]\displaystyle \left(\frac{7}{6}\right) -1 = \frac{y}{x}[/tex]
Subtract:
[tex]\displaystyle \frac{y}{x} = \frac{7}{6} - \frac{6}{6} = \frac{1}{6}[/tex]
Therefore, our answer is B.
Please help me ASAP I’m stuck on these questions
Answer:
4, yes through the middle 5, yes through the middle 6, yes through the middle all of them reflect from the center
Step-by-step explanation:
i have 17 coins. N of them are nickels and the rest are dimes. write an expression in two different ways for the amount of money that i have
Answer:
Step-by-step explanation:
(N)0.05 + (17-N)0.1 = M; M = amount of money I have.
Or 1.7-0.05N = M.
An expression two different ways to the amount of money is equals to
1. 5N + 10 (17 -N) = Y cents
2. N + 2(17 - N) = Y nickels
What is amount?
" Amount is defined as the total of any given quantity."
According to the question,
Total number of coins = 17
Number of nickels coins = N
Number of dimes coin = 17 - N
'Y' express the amount of money
Represent amount of money in cents
1 dime = 10 cents
1 nickel = 5 cents
Expression to represents amount of money in cents,
5N + 10 (17 -N) = Y cents
Expression to represents amount of money in nickels,
1 dime = 2 nickel
N + 2(17 - N) = Y nickels
Hence, an expression two different ways to the amount of money is equals to
1. 5N + 10 (17 -N) = Y cents
2. N + 2(17 - N) = Y nickels
Learn more about amount here
https://brainly.com/question/27337635
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